Cooperative and Competitive Games: Game Theory & Evolutionary Biology
How do cooperative and competitive behaviours arise in nature? Are they in tension and will human systems evolve more toward one than the other?
Cooperation and competition are behaviours that emerge, as far as we can tell, only in living systems. The question we have to ask ourselves then is, why do living systems in contrast with other physical systems exhibit these behaviours?
An obvious answer is that living systems, unlike other physical systems, are normatively coupled with their environments. This means that they display an internal preference for certain outcomes over others. What outcomes precisely? Simply put, survival enhancing ones: procurement of nutrients, avoidance of predators, and reproductive success. But clearly these do not exhaust the observed behavioural preferences across species. Sometimes individuals or groups behave in ways that appear to contradict their reproductive imperative. Are these instances explainable by virtue of the same mechanisms or do additional explanatory factors also play a role? When it comes to humans in particular, the behavioural landscape becomes tremendously complex. Do the conditions that yield competitive or cooperative outcomes in other species also equally explain human cooperative and competitive schemes or should we seek recourse to additional factors to explain the degrees of cooperation and competition present in human collectives?
The best explanation that we have for this preferential constitution of living organisms is the process of evolution by natural selection. Since the traits of organisms are functionally equivalent to their survival toolkits, they can be described in terms of their fitness. Functionally speaking, fitness is an individual’s probability of reproductive success. Fitness, therefore, is a function from an individual and its environment to its reproductive outcome. As such, fitness implies that living organisms contend with their environments. And since the environment consists not only of physical but also population characteristics, the behavioural landscape bifurcates across a spectrum of cooperation and competition.
Natural selection alone, however, does not quite get us out of the explanatory quagmire. How are we to conceptualize the units of cooperation and competition to begin with? In some sense, nature has done the work for us since most individual organisms are organized as discrete functional wholes. Since most multicellular organisms consist of smaller subsystems of cells, we can infer that multicellular organisms function, for the most part, as cooperative units. This is not to imply that elements of competition are entirely absent within organisms. Rather, the haploidy nature of the somatic line precludes any strong motivation for defection due to genetic similarity. In addition, even simple prokaryotic organisms like bacteria exhibit predation.
This, however, does not explain how multicellular organisms evolved to begin with. No consensus prevails over what caused multicellularity, though some suggest the possibility of multiple independent origins across clades (Niklas & Newman 2020). Inter-organismically, meanwhile, cooperation appears to increase proportionally to genetic-relatedness and vice versa apart from reciprocally altruistic acts that operate less strictly on genetic relatedness and more strongly on acts of reciprocity. However, the kin-selection hypothesis may not suffice to explain observed group behaviours that appear inconsistent with exclusively gene-centric explanations. Furthermore, do evolutionary favourable conditions for cooperation exhaustively explain human sociality? Or have humans evolved cooperative mechanisms that transcend mere kin-selective and reciprocally altruistic schemes?
Since cooperation is the relatively rarer phenomenon, and competition much more so the rule, we will delve into conditions that yield cooperative outcomes and attempt to scaffold our explanations to human collectives. We will begin with evolutionary underpinnings, move on to game-theoretical conceptions of group interaction, consider relationships between zero-sum and non-zero sum games, and finally end on observations about the possible evolution of human collectives toward more or less cooperation.
Natural Selection
However way life on earth began, organisms occupy environments surrounded by intra and inter-species populations in the larger ecology. Because interactions between and within species result in survival enhancing or diminishing effects, it gives us a basis for understanding competitive and cooperative behaviours.
Evolutionary biologists define competition as an interaction between individuals of the same or other species where resources used by one are made unavailable to others. Conversely, they define cooperation as interactions that enhance the survival of the interacting species. To avoid equivocation on the uses of the terms competition and cooperation in the scientific literature, I will deploy these terms broadly as just defined, though as we will see necessary conceptual nuances may cast doubt on whether grouping biological behaviours into these two broad camps is cogent.
When competition occurs between members of the same species, it’s termed intraspecific and when it occurs between different species it’s termed interspecific. Since competition is a function of resource removal, it is greatest where there’s resource overlap. Competition can be further operationalized into direct and indirect interactions. Indirect interactions, also called exploitation, involve the removal of resources without individuals of the same or different species being in direct physical proximity. On the other hand, interference occurs when direct interactions between individuals result in harm or prevention of access to resources.
Other types of interactions include predation, parasitism and mutualism, the latter being cooperative or reciprocally exploitative. Predation involves consuming individual prey, parasitism involves an asymmetrical relationship where a parasite obtains nutrition from a single host but confers no advantages in return, and mutualism refers to interactions between species that mutually enhance survival and/or reproduction (Futuyma 2006). Parasitism exists on a spectrum with predation and grades on predation at its extremes (Ibid).
There are unresolved questions regarding how to characterize these interactions. For example, some forms of symbiotic mutualisms exhibit such a high degree of host specificity, that the two species are sufficiently physiologically integrated to constitute a single organism (Futuyma 81). In fact, one of the hypotheses for the evolution of eukaryotes holds that the mitochondria and other organelles in the eukaryotic cell were independent prokaryotic organisms that combined in an endosymbiotic manner to constitute a single organism. This may also hint at possible explanations for the emergence of multicellular organisms: mutualistic conditions favoured the emergence, broadly speaking, of internally cooperative structures such as ourselves. However, our internal cooperation — namely our constitution as a single organism — is plausibly an artifact of the reproductive mechanisms of the constituting cells of systems in our bodies, namely by mitosis or division (where daughter cells inherit the same genetic inheritance). Whereas the reproductive mechanism of the organism as a whole is by meiosis, which yields offspring that have the composite/recombinant DNA of half of each parent.
This strategy yields both genotypic and a fortiori phenotypic variations that enhance adaptability, but also creates the stage for intraspecific competition when the genetic distance is sufficient. The kin-selection hypothesis construes most forms of intraspecific cooperation as a function of self-similarity, namely as directly proportional to genetic relatedness and inversely proportional to genetic distance. There’s a large body of evidence corroborating this hypothesis, wherein individuals are more likely to cooperate with their relatives. Explanations for kin selection vary from direct to indirect fitness-conferral: that is to say, certain cooperative behaviours like helping or sticking with the pack may be selected for because they benefit the individual directly (short-term) or indirectly (long-term). But as we saw, interspecific mutualism is another, altogether different type of cooperative strategy not rooted in genetic-relatedness. This doesn’t imply that a mutualistic relationship between two species may not be a genetically encoded adaptation, merely that the conditions of its inception and future sustenance are rooted in mutually increased fitness.
It is a matter of debate whether mutualism and kin-selection exhaust the cooperative strategies found in nature. Another candidate known as group selection has been proposed, which suggests that sometimes individuals sacrifice their fitness for the benefit of the group. This is not to be confused with the kin-selection hypothesis, which as we saw roots intraspecfic cooperation in genetic similarity. In the kin-selective scenario the individual always behaves selfishly in the sense that it promotes the inclusive fitness of its genes. Inclusive fitness recedes proportionally from an individual’s offspring to its relatives. By promoting the success of its kin, the individual concomitantly promotes the success of a proportion of its genetic makeup. Group selection, meanwhile, refers to scenarios where an individual sacrifices their fitness (inclusive or not) for the benefit of the group (incurs more costs than benefits, at least in the short run, to itself). That group selection constitutes a genuine phenomenon is a controversial and, for the most part, fringe view in evolutionary biology because it implies that selection may also occur at the level of the group instead of merely the individual.
When we scaffold to human collectives, the tensions between purported adaptations like group and kin selection further exacerbate. That is to say, the cooperative and competitive landscape becomes more difficult to explain and parse into intelligible taxa. This is, in part, because the spectrum of possible behaviours and conditions consistent with fitness are much broader in human systems largely due to human differentia like language, thought, ultrasociality, and cultural transmission that enable vastly more powerful levels of ecological niche construction. One question worth pursuing is whether human cooperative schemes and behaviours are exhaustively explained by kin-selective and mutualistic strategies or whether sufficient disjunctions persist from these evolutionary strategies that cannot account for human cooperative achievements. A parallel question is whether there are grounds for revising our conception of the units of selection as being exclusively genes.
The proposed alternative to gene-selectionism is multi-level selection. The central thesis of multi-level selectionism is that natural selection acts simultaneously across organizational scales from cells and individuals to groups (Kramer & Meunier 2016). Notice that even with multi-level selection, the mechanism of genetic transmission does not change. However, it does mean revising the Weismann barrier to account for heritable epigenetic factors. The Weismann doctrine posits a strict separation of the germ and somatic lines, wherein hereditary information flows directionally from the genome to the soma, or from DNA to RNA expression, and not vice versa (Bline 2020). Since then, several extra-genetic mechanisms have been shown to impact phenotypic heritability such as regulatory gene products being transmitted trans-generationally (Joblonca 2009). In effect, environmental cues that affect gene expression in one generation can be transmitted across succeeding ones without affecting the DNA /nucleotide sequence.
The motivation for advancing an alternative to gene-selectionism like multi-level selection rests with the former not being able to explain observed spectra of altruistic and cooperative behaviours that contravene its predictions. Individuals may be selected for altruistic and/or group conformist traits, which in turn increase the total fitness of the group. However, many wrinkles remain to be ironed out in this picture. For example, it remains unclear whether phenomena like eusociality observed in at least some insects and crustaceans can be entirely explained within a kin selective framework. Eusocial arrangements exhibit cooperative brood care and a division of labour between reproductive and non-reproductive castes. Kin-selection and inclusive fitness models explain these features within a gene-centric framework, wherein non-reproductive casts promote the genes of kin. However, if inclusive fitness sufficed explanatorily, haplodiploid species should be more likely to form eusocial colonies, which has not been observed to be the case thereby suggesting that factors other than genetic-relatedness must also play a role(Wilson 2005). Multi-level selection posits between-group competition as a plausible structural condition for the emergence of eusociality, wherein in-group altruism enhances group differential success relative to another.
Problems persist with formalizing multi-level selection, however. First, multi-level selection suffers from an ambiguity of definition. The theory bifurcates into conflicting definitions of group and group selection: 1) MLS-1, where “group fitness is defined as the average total fitness of constituting organisms” and a group as a set of interactive individuals that influence each other’s fitness and 2) MLS-2, where “group fitness is defined as the expected number of offspring groups, where groups are typically geographically discrete, multi-generational and reproductively isolated” in attempt to explain group level events like fission and extinction (Kramer & Meunier 2016). Some models construe MLS-1 and MLS-2 as diachronic phases, whereas others as incompatible models of multi-level selection. The former deploy MLS-1 and MLS-2 as sequential steps that may explain the evolution of multicellularity, which we isolated at the outset as an explanandum in need of an explanans in order to understand the dynamics of cooperation and competition in nature. MLS-1 involves an alignment of fitness phase, where cells establish a cooperative and communicative framework on the basis of genetic self-similarity (Nicolas & Newman 2020). MLS-2 involves an export-of-fitness phase, where cells achieve a level of interdependence wherein fitness is exported to the colony or cooperative unit rather than operating at the individual level (Ibid). Most studies suggest many contingent paths can lead to the evolution of multicellularity, but these likely share the phase transitions just described (Ibid).
Notwithstanding the contested compatibility of MLS-1 and 2, some suggest that at least MLS-1 is formally equivalent to kin-selection, which would render it explanatorily redundant. This charge of formal equivalency rests on the fact that both theories when sufficiently generalized predict that social or altruistic behaviours increase the inclusive fitness of individuals when between-group selection is stronger than within-group selection (Kramer & Meunier 2016). The charge of formal equivalency is highly contested, however, on grounds that group selection effects do not perfectly overlap with generalized kin selective ones. Furthermore, some argue that the generalized kin-selection framework cannot account for long-term, asynchronous group events like fission, fusion, and extinction (Simon & Fletcher 2012).
Finally, it remains highly controversial whether human ultrasociality, the ability of humans to participate in large-scale collective action, should be understood within a spectrum of weak eusociality or whether additional mechanisms are required to explain human cooperativeness. While eusociality bears structural similarities to human collective arrangements and common population-dynamical causes should not be dismissed outright, it does not suffice to explain key features of human cooperative schemes (Abbot 2011, Heath 2011), whose forms are heavily underdetermined by the evolutionary inheritance. Gene-culture co-evolution, also known as dual-inheritance theory, which posits reciprocal causation between genetic evolution and cultural evolution, fills in many of these explanatory gaps. According to this theory, cultural inheritance undergoes selective pressures analogous to natural selection (Gintis 2011).
This model suffers somewhat from a chicken or the egg problem or begs the question with respect to the origin of human culture. Cultural evolution can only occur through mechanisms of inter-generational transmission, which are arguably made possible by differential features of human cognition (though others posit strong imitability as the originating factor). However way these evolved, they enabled a multiplicity of social arrangements relative to our biological inheritance. In other words, many of the features of human culture cannot be explained by virtue of biology alone, but must also seek recourse to culture-specific norms and ideological frameworks.
According to Heath (2011), kin-selection and reciprocal altruism do not suffice to explain the degree of cooperation exhibited in human collectives, particularly organizational features like states and large-scale collective action. Nor should we default to group or multi-selective frameworks because these can be highly unstable when within-group competition is stronger than out-group competition (this, however, is contestable). Rather, the explanatory ingredient rests with an adaptive trait of norm-conformity that does not inherently favour cooperative or selfish behaviours, but flexibly biases the individual toward group norms (Heath 2011). The latter explains the possibility that celibate casts can reoccur across iterations of a culture despite not being heritable.
Given the cultural datum, it has to be the case that not only do individuals absorb the selective pressure of its environment at different compositional levels, but these levels also often conflict with each other, thereby explaining the vast spectrum of observed human behaviours. Heath and others, cash out these different selective pressures by drawing a distinction between cultural and reproductive fitness as sometimes diverging constraints (Heath 2011). For example, celibate priestly casts satisfy a model of cultural fitness, while not satisfying reproductive fitness. The urge to reproduce conflicts with the disposition to function as part of the clergy.
Heath explains the foregoing tension by arguing that a disposition for norm conformity is a hard-wired adaptation (with “hardwired” defined as probability-raising rather than determining). This norm-conformity bias then fluidly takes the shape of different cultural containers. According to Heath, the genetic inheritance can be viewed as a set of biases that can be overrode, within limitation, by culture. It is the qualifier “within limitation”, however, that is not allotted sufficient consideration. The norm-conformity disposition could only have evolved in case it conferred adaptive benefits that outweighed its costs. It is not an accident that most cultures and belief systems share certain large-scale constraints while exhibiting wide variation peripheral to those constraints. While nature and culture can vary independently within some critical threshold, the general pattern is that the biological inheritance, even taking into consideration its phenotypic plasticity, forms the centre of gravity that circumscribes the fuzzy boundary of cultural variations until we succeed in reengineering or overwriting it entirely. In light of this, cultural norms and belief-systems must submit to indirect selective pressures, even if these are consistent with a wide array of expressions. Far from subjecting cultural norms to “just-so stories”, the coevolutionary thesis provides the explanatory framework for the wide diversity of human behaviours but does not at the same time provide the tools for explicitly adjudicating questions of causal priority or equiprimordiality that remain empirically unsettled like the evolution of language, intentionality, and higher-order thought (all of which contribute to the accumulation of cultural inheritance).
To return to an earlier example, celibate clergy could never comprise the entire population, but they can be nursed within a culture precisely because the reproductive wherewithal of that culture affords them as collateral. This is not to suggest that they function as collateral but rather that whatever cultural function they serve if they do at all (e.g. as stewards of norms etc), it may indirectly increase the net reproductive fitness of the culture or group by fostering stability or solidarity. That is to say, it is possible that individual costs to their reproductive fitness are disproportionally translated into benefits to the net reproductive fitness of the group. While caution is recommended when advancing such overtly functionalist explanations, they should not be outrightly ruled out either.
Having considered the evolutionary origins and limits of human cooperative schemes, let’s now turn to theories that aim to formalize human action and decision within the narrow prism of self-interest, known as game theory.
The Intractability of Rational Choice
Rational choice theory is a theory of human decision or decision theory that aims to formalize an instrumental conception of rationality. In a nutshell, instrumental rationality is the view that rational deliberation subserves an agent’s ends. This view is nested in a theory of both human motivation and cognition that posits certain mental representations like desires and beliefs. Desires are ways we’d like the world to be, while beliefs assumptions we make about the way the world is, will be, or could’ve been. In philosophical terminology, these are termed intentional states because they are directed at the world as attitudes about states of affairs or facts. They also exhibit opposite directions of fit, with the former being prescriptive, and the latter descriptive. If desires are conceptualized as preferred outcomes, then beliefs can be conceptualized as instrumental constraints in bringing about these outcomes as efficiently as possible. A concomitant assumption to this view of rationality is non-cognitivism about ends: ends are not objectively discovered or a feature of reason as such, but arise variously in agents from extra-rational causes. Under this conception, rationality consists of the deliberative constraints that satisfy desires or ends, but the latter need not be rationally grounded. Rationality is thus instrumental in the sense that it’s nested within, or subordinated to, extra-rational ends.
Assuming then that agents prefer certain outcomes, the purpose of practical reason is to select actions that have the highest probability of bringing about the preferred outcomes. If we think of the agent’s rank-ordered preferences as the desired outcomes, then instrumental rationality should supply a utility-maximization function for realizing them according to their subjectively weighted priorities. The utility maximization function is nothing short of the procedure for selecting the right action(s) given agential doxastic (belief) and preferential (desire) constraints (as the antecedent psychological ontology of actions).
The decision-procedure can be visualized through hierarchical decision trees comprising states, actions, and outcomes. States represent ways the world is configured, actions represent available choices given some variable state, and outcomes represent effects of actions. Given that any of the states obtains with some differential probability, we can visualize the agent’s choice space via three actions with variously weighted outcomes.
Given these assumptions, the utility of each action branch in each state can be computed through a decision-procedure, which can be formalized as a function that takes as input the sum of all products of the utility of an outcome (standardized as an integer between 1–10 and ascribed by the agent) and the conditional probability of the outcome given some action, to yield as output the net utility of that action:
u(a) = ∑ p(o|a)u(o)
The paradigmatic formalization of the utility-maximization function is known as the von Neumann-Morgenstern procedure. In this procedure we collapse desires into preferential outcomes, and remain agnostic about the ultimate causes of the preferential distribution over outcomes. We’re left then with these minimal assumptions: agents instrumentally pursue the good, about which we remain agnostic and do not further analyze, relative to their beliefs.
The context of individual agents, however, becomes complicated when other agents enter the picture. These complications become apparent when we apply the decision-procedure to a minimal system comprising two agents. We said that agents must assign probabilities to states in order to select an action. However, when two agents are involved, each must assign probabilities to the belief-states of the other. This implies that the actions of one agent are belief-states for the other and vice versa. Think of it this way: in order for you to select an optimal action, you must ascribe a probability to the other agent’s optimal decision-choice. Conversely, in order for them to select an optimal action, they must also ascribe a probability to your optimal decision-choice. If we now try to compute the utility-maximization function, it leads to an infinite regress of anticipations (Heath, 27). By ascribing the agent states, I also have to account for their anticipations of my states, which in turn changes my state, but also changes theirs and so on leading to an infinite regress.
Game-theoretical models strive precisely to solve these kinds of rationally intractable problems that arise in social action-contexts. Game-theoretical solutions famously aim to model belief equilibria among agents, wherein each agent ascribes some probability to the other agent’s future actions. When we do this, we find that some game theoretical models with two or more players are solvable in the sense that when the outcomes of all the possible conditional state-action paths are computed, there’s one optimal choice for one of the players that dominates the strategy of the other players. We call these games strongly dominated and can represent them via matrices:
Whenever an agent’s strategy is the best response to other agent’ strategies, in other words it’s not self-undermining, we call that an equilibrium, and specifically a Nash equilibrium after John Nash who proposed that utility-maximization leads to stable equilibria of choices among agents as solutions to game-theoretical quandaries.
However, not all games are dominated in this way. Some games, such as the well known Battle of the Sexes, yield two equilibria — so it’s stable, but not convergent, since there’s no single solution to the game. Other games are neither stable nor convergent. With these games there’s no internally consistent solution that eschews the infinite regress. Consider the matrix below:
Nash’s solution to these quandaries was to propose mixed-strategy equilibria: equilibria where the outcomes are not only pure like (U,R) but over the set of randomizations of all possible outcomes including fractional distributions of strategies (3/10 U, 7/10 R). These solutions solve the regress of anticipations problem but also proliferate the possible equilibria. While caveats and controls that aim to reduce the number of equilibria can be introduced, such as avoiding zero-probability events, the problem with these strategies is that they mobilize the rational calculus toward an equilibrium solution, but fail to prescribe rational agents with choices that maximize their ordered preferences (Heath, 33).
Nash’s solution to the equilibrium selection problem appears, therefore, to be ad-hoc when it comes rational choice. A further blow to this programme occurs when you solve for multiple iterations of a single game, which mathematically yields a hopelessly large number of equilibria. Furthermore, across infinite iterations or finite iterations with an uncertain terminus, the number of admissible equilibria balloons to infinity (Heath, 34).
Introducing communication into the system relative to some compositional language does not mitigate these results, but exacerbates them. The problem of neologisms illustrates this. Messages not anticipated by an agent are de facto reduced to zero-probability events by the equilibrium-solving procedure regardless of what meaning the agent ascribes them, thereby not screening them out from the set of admissible equilibria (Heath).
The intractability of rational choice, that is to say, the failure of the game theoretical programme to formalize instrumental rationality over multiple agents generalizable to social collectives leaves the phenomenon of social order across human collectives unexplained. A theory of action that can account for the degree of coordination and cooperation exhibited by human collectives must seek recourse to additional psychological and mental tools.
Parsing Zero-Sum from Non-Zero Sum Games
The stage of cooperation and competition can be elucidated by the notion of a zero-sum game. Zero-sum games are games wherein the advantage gained to one party translates in a loss to the other. Zero-sum games are common in everyday situations like traffic, when we compete for a job promotion or competitive games like chess. To elaborate the first example, consider traffic situations where time is scarce such as when you’re rushing to get to work on time. If you let other people cut you off, you might forfeit being on time. You might even speed a little. Now imagine another driver in the same situation as you. Incentive for non-cooperative behaviour significantly increases when traffic undercuts the time-sensitive goal of getting to work on time.
Each of the enumerated examples have something in common: the prize is scarce, and not all those who compete get to win it. With some caution, this condition of scarcity can be generalized to all the goods towards which organisms strive. However, it isn’t at all obvious how scarcity should be conceptualized. For example, it is uncontroversial that species compete for mates and resources. The use of “compete” in this sense need not imply aggressive or hostile behaviours, merely a combination of random and adapted behaviours that result in reproductive success. However, the iteration of this process may then select for traits that outwardly display intra or inter-species hostility. In this picture, competition emerges from an imbalanced supply-to-demand ratio of preferred resources. The causal direction for competitive behaviours and traits flows from the environment to the species. But what if the availability of resources neither strongly favours a cooperative or competitive strategy?
For example, when a company seeks to enter a market, a reasonable assumption is that demand for a product is finite. But this does not factor the possibility of increasing absolute demand by changing consumer preferences. Economists compute demand as proportional to a utility function, which measures consumer satisfaction. Yet consumer satisfaction is highly malleable and varies considerably across personal preferences. You can argue with great plausibility, to take two random examples, that fridges and personal computers greatly increase personal utility. At the same time, they decrease the utility of a survivalist who wants to live through hunting and remain disconnected from broader civilization. Statistically, however, personal preferences are heavily constrained by networks of dependency embedded in civilizational infrastructure relative to its technological wherewithal. It is possible but really costly for the average person to opt out of owning a personal computer or a fridge. The average optimal utility function, therefore, is fundamentally in flux relative to the evolution of a culture.
It is hardly contestable that cultural transmission and modern economic organization have increased the absolute wealth and resources available to humans. Assuming some minimum threshold of distribution, this also implies that the absolute wealth of living individuals has also increased. By the same token, it can be argued that ecologies and evolutionary systems also increase the absolute availability of resources by complexifying chains of dependency. In some respects, the eukaryotic revolution enabled the vast phylogenetic expansion of taxa by innovating a recombinant reproductive mechanism that enhances adaptability. On the other hand, it is conceivable that structural features of both ecologies and human economies could lead to races to the bottom, extinction or mutual destruction. The latter is uniquely exacerbated in human systems.
Genuine zero-sum games require outcomes with winners and losers, where some mutually desired good cannot be distributed equally amongst all the players. While genuine zero-sum games arise because of limited supply of some desired good, individual zero-sum games always take place within a wider game of life. While exhibiting greater degrees of freedom, in the long run the game of life can also be conceptualized in zero-sum terms. One way to do this is to frame the set of all iterated games as either conducive or not conducive to reproductive success. Setting reproductive success as the ultimate measure given the sexual preferences of humans can be either a high or a low bar: a low bar when reproductive outcomes are distributed more equally and a high bar when that distribution tips to the tail ends. This picture, however becomes complicated when the possibility of group or multi-level selection is considered. Within this framing, individuals can also win the game of life by promoting the overall fitness of the group. Notwithstanding difficulties of defining the group (in biological terms the most predictive definition is proportionality to genetic-relatedness, while in human systems circumscription of group boundaries exhibits far greater flexibility due to our ability for abstraction, which in turns enables us to transcend mere genetic-relatedness), human definitions of the good can become genuinely unmoored from their biological tethering. And, as we argued earlier, cultural preferences can to some extent vary independently from biologically inherited preferences. (Some have attempted to explain this phenomenon in terms of group selection and/or within a spectrum of eusociality, whereas others through purely social mechanisms that are not necessitated by an underlying biology.)
The question whether the zero-sum schema applies broadly to social collectives and complex systems like ecologies and economies is tantamount to computing the aggregate utility function for all the entities that exhibit preferences over outcomes. This utility function becomes increasingly intractable when you account for the fact that preferences at different organizational units can conflict. In human systems, some of these conflicts can be avoided through cost-benefit analysis. For example, in situations with high uncertainty, the optimal preferential outcome is sublimated to secure a scenario of collective equilibrium.
The oft-touted schema of non zero-sum games is the Prisoner’s Dilemma. In the Prisoner’s dilemma, two criminals are captured and, unbeknownst to each other, offered two options: they can betray the other on the bargain that they be let free or choose to remain silent for a reduced sentence. Given that neither knows what the other will do, there’s a matrix of four possible outcomes. If both prisoners choose to remain silent, the prosecutors won’t have enough evidence to convict, but each will be given 1 year on a smaller charge. If both defect, then each must serve two in years prison (securing a reduced sentence for informing). However, if one defects but the other stays silent, the defector gets out scotch free, and the other serves 3 years in prison.
The mutually cooperative outcome incurs less costs than the mutually uncooperative one, where each prisoner seeks to maximize their self interest. The significance of the Prisoner’s Dilemma rests on its generalizability to collective action problems in human collectives. Even though the only possible Nash equilibrium in finite repeated prisoners’ dilemmas is to defect every time, empirically humans display a systematic disposition to cooperate (Kuhn 2019). Axelrod (1984) also found that over the long-run cooperative strategies trumped uncooperative ones. Curiously, humans tend to cooperate in one-shot prisoner’s dilemmas, just as they do in iterated ones, though the latter can veer toward greediness depending on the tendencies of players. Axelrod (1984), for example, found that mixed-strategies fared best in order to sustain cooperation while at the same time reducing the chance of being exploited.
Prisoners’ dilemmas default to evolutionary stable strategies insofar as participation delivers the advantages of cooperation, which is to say that the conditions of mutual benefit are replicated. This tendency to cooperate may be filtered through a more general norm-conformist disposition, but it is also highly contingent on an overall system of reciprocity. In situations where participants do not stand to gain an advantage from cooperation, they are much more likely to withdraw from cooperation. However, the overall picture is much more complex. In the case of humans, mixed strategies and asymmetrical payoffs are common. Given that most social interactions occur in complex networks with varying distributions of bargaining power, most individuals modulate their cooperative strategies relative to their status and calculations of short-term and long-term payoffs. Individuals with greater bargaining power, for example, may opt for a symmetrical payoff on the basis of their calculation of the likelihood of a reversal of fortunes, but statistically they are likely to seek asymmetrically favorable payoffs. Ultimately, strategies deployed by individuals are relative to the informational complexity they bring to bear (consider perfectly rational Bayesians as an abstract ideal), which determines their ability to learn from past interactions and accuracy of foresight. Cooperative strategies are therefore always preferable so long as they increase fitness, whether short or long-term.
It bears mentioning that the overarching game that the human being plays is the status game. The status-game is a proxy for reproductive success (assuming status is highly correlated to availability of resources), even though it can become co-opted by culture toward games that do not ultimately result in reproductive success. Proximally and for the most part, most socially sanctioned status games are good heuristics for reproductive success. Filtered through the prism of human differentia, status-games can lead to intra-generational novelty that can ultimately increase the size of the pie, but more importantly, human status-games drive the increasing differentiation and complexification of spheres of competence. In this sense, status-games are not ultimately zero-sum, even though the allotted positions of high status in any given social configuration are as a rule in short supply. This is due to the fact that even if the net status distribution of a population increases, relative status still accrues to the top because of an intrinsic preference for positional goods. Positional goods, which are goods valued because of their limited supply, acquire their value relative to the internal norms of a culture thereby enabling status allocations to exhibit significant variation. The intrinsic preference for positional goods is likely a byproduct of a disposition to conceptualize status as being in short supply. This, in turn, may be an artifact of our evolutionary inheritance that also encoded competitive and selfish behaviours as survival-enhancing adaptions in resource-scarce environments.
Even though most games are in an ad-hoc way zero-sum, the human being participates constantly in redefining or expanding competency games thereby rendering ultimate outcomes as essentially open (especially if the game is construed inter-generationally). The ultimate openness of outcomes could be countered by adherence to some form of strong determinism, wherein possession of perfect information yields perfect predictions. In this universe, perfect agents compete for overlapping finite outcomes given inexorably increasing total entropy. Strong determinism, however, is very likely false in our universe. Even so, the default interpretation of entropy nonetheless puts a damper on the ultimate openness of outcomes by limiting the availability of energy across infinite time. The same argument can be extended to nature at large, wherein the evolving ecology produces novelty by complexifying the web of interdependence. While humanity has recently grown to dominate the ecology, at some level of description there’s no fact of the matter as to what the unit of replication really is because any individual can be instrumentalized toward the propagation of some whole at the expense of itself or selfishly propagate itself at the expense of others.
Trustless Cooperation
In our time, increased digital participation continues to alter the social fabric and the methods through which individuals and groups associate and transact with one another.
An interesting feature of political culture and broader social discourse is the way that the values of cooperation and competition seep into political ideologies. This is evident in disagreements about what should be state controlled versus privately held and the role and extent of state interference in civil society. In societies with strong rule of law traditions, legislative history reflects this complex relationship between public institutions and private enterprise. Sometimes the legislative landscape nurses a symbiotic or mutually beneficial relationship between these sectors, and other times the distribution of control creates inefficiencies that require legislative correction. For example, deregulating banks in the United States contributed to the 2008 Financial Crisis, something Canada averted thanks to stronger regulations in that sector. On the other hand, examples abound of state-owned enterprises routinely failing to fulfill their public-interest mandates and losing money due to lack of accountability or crashing into insolvency. In Canada this is exemplified by the deregulation of Air Canada in the late 1970s and later full privatization in the 1980s.
A prominent battle today between cooperative and competitive values wages on the ownership of software. The open-source movement, emerging from academic values of cooperation and collaboration fostered in computer science departments in the early days of computing, promotes free and modifiable software not restricted by copyright. The private sector, on the other hand, produces for-profit proprietary software. Strangely, while conflict persists between these spheres, regions of symbiosis have evolved in an ecosystem that nurses both open-source collaboration and proprietary products. For example, companies routinely make certain products open-source (e.g. Google making TensorFlow open-source), while open-source products become proprietary to remain viable. The general trend, however, is hard to overlook: open-source products enjoy less support, may be of lower quality, and respond less readily to market forces. This is not surprising considering the different incentive systems that each of these spheres enjoy. Nevertheless, this is not always the case and depends on the ecosystem behind a software and whether the products are in direct competition or not. As a form of crowdsourcing, open-source has evolved to nurse consensus-based mechanisms of accountability. On the other hand, without proprietary software, few developers would have jobs and therefore resources to contribute to open-source products. Furthermore, a hybrid strategy has become dominant where companies seed adoption through free versions of their products in order to then increase the likelihood of selling their premium ones. In other words, the threads of cooperation and competition are messy and interlocked, and continue to evolve within a coexistence that often fosters desirable outcomes to all parties.
This was none more evident than with the release of the first distributed ledger cryptocurrency, Bitcoin, as an open-source software in 2009. Because the code that made it possible, a public distributed ledger called a blockchain was not copyrighted, it spawned a large movement and today growing ecosystem of cryptocurrencies and applications that run on variations of the blockchain code. However, blockchain applications that could, in principle, supplant corporate ones that dominate the app landscape have not yet seen mainstream adoption. Some of the problems that beset the mainstream adoption of decentralized apps lie with their internal governance and decision-making processes, the capacity for and pace of iterative design, and appeal to mainstream users. To illustrate, consider the case of Steemit, a social media dapp that incentivized users, both “curators” (voters) and “creators” (content generators), to participate via tokens that are exchangeable for currency. The system that Steemit had devised by controlling the daily supply of Steem tokens, which can be converted to Steem power (increasing the weight of certain voters) or Steem dollars (which are convertible to real currency), was too complicated for the average social media user. If you contrast this system with the expedient “likes” and posting process in popular apps like Instagram, it becomes clear that the effort threshold for participation is much higher in Steemit. Interestingly, this bears uncanny parallels to some of the pitfalls of the political ideology of social anarchism. Anarchists consider all hierarchies as prima facie illegitimate, and prefer flat structures of popular participation and governance. However, in any working model this greatly exacerbates individual responsibility to the point where most people would be loath to participate. If dapps want to solve this problem, they have to find a way to lower the threshold of participation to almost trivial levels, like most apps do. The cost of doing so however is that it undercuts the utopian dream of converting the labour of users to their direct benefit.
This is fine and well on the user end, but let’s consider the consensus mechanisms of distributed ledgers and what they mean for popular participation and decentralized systems at large. In the intervening years since the invention of blockchain, two chief consensus mechanisms have dominated the landscape: proof-of-work and proof-of-stake. Because blockchain ledgers are distributed, the method of full participation requires that each participant store a full node of the entire blockchain on their servers, and for any new transaction that creates a new block, all the nodes have to agree before that block is verified. Because hosting a full node is already a high threshold of participation, cryptos and dapps allow for light grades of participation, where users can transact by either verifying only parts of the ledger or by altogether outsourcing the verification process to a full node.
In principle, anyone can be a full node, but in practice the participation requirements inadvertently favour a certain class of people, i.e. at the very least those who can afford it monetarily and time-wise. This participation bottleneck is either heightened or loosened by the consensus mechanisms. Proof-of-work places the barrier of participation on computational power, wherein each new block requires the computation of an immutable hash function. Because a ledger increases with time, the computational power required to sustain the creation of new blocks also proportionally increases. These energy inefficiencies are rectified by the proof-of-stake mechanism that does not mandate a computationally taxing algorithm for the creation of new blocks, but rather places the weight of participation on a minimum threshold of crypto tokens owned by the participant. In other words, those who want to own a full node must also have a sufficiently high stake to be able to do so. On the one hand, a sufficient barrier of participation ensures the trustworthiness of the blockchain, and on the other, these mechanisms inadvertently create a distributed class of individuals who disproportionally wield power over the (governance of the blockchain) non-full node users.
These problems aside, it is worth appreciating the potential for cooperation that the blockchain creates. At least in principle, it promises to undercut the exploitative asymmetry between private citizens and corporate actors that has become greatly exacerbated in the last two decades. It is worth pondering deeply the extent to which the tech world has managed to both disrupt and commodify social processes upon which personal lives and goods are staked. By enlisting large-scale participation of the population in their apps, modes of in-person romantic courtship, for example, have nearly disappeared in favour of dating apps. Not only this, but entire attention economies have been created through increased social media participation, wherein the affordances of interaction and participation are entirely engineered and controlled by these corporate actors. In other words, in some very concrete sense corporate apps hijack the agencies and attentional resources of users to their disproportional benefit. Blockchain technology and the dapp movement could in principle offset some of these exploitable relationships by creating a parallel ecosystem of participation that does not deploy exploitative and addictive digital affordances.
Just as the evolution of corporate actors is a recent (last two hundred years) social phenomenon that both contributes and oftentimes severely undercuts the public good, so the potential for creating more robust and less exploitative cooperative schemes may be inscribed in certain digital technologies that could offset rather than exacerbate the conflicts of interest that beset the current social and civil landscape.
Non-Rational Games
“All that is here related moves with imaginary feet along the parallels of dead orbs; all that is seen with the empty sockets bursts like flowering grass. Out of nothingness arises the sign of infinity; beneath the ever-rising spirals slowly sinks the gaping hole. The land and the water make numbers joined, a poem written with flesh and stronger than steel or granite. Through endless night the earth whirls toward a creation unknown…”
— Henry Miller, The Tropic of Cancer, p. 252.
Notwithstanding difficulties in delineating the boundary between rational and irrational as far as concerns practical reason (it’s arguably easier when it comes to alethic modalities), the human being is uniquely equipped to knowingly extricate itself both from socially sanctioned games and unadulterated self-interest. This strange possibility suggests a set of outcomes that are neither rational in the strict sense nor non-rational in the sense of genetically programmed heuristics, but genuinely intentional irrational pursuits. Perhaps what these games share in common is the elevation of the absurd as an organizing principle akin to what the Dada art movement did in the early 20th century.
Selected Bibliography
Adami, Christoph, et al. “Evolutionary Game Theory Using Agent-Based Methods.” Physics of Life Reviews, vol. 19, 2016, pp. 1–26., https://doi.org/10.1016/j.plrev.2016.08.015.
Alexander, J. McKenzie. “Evolutionary Game Theory.” Stanford Encyclopedia of Philosophy, Stanford University, 24 Apr. 2021, https://plato.stanford.edu/entries/game-evolutionary/#HistDeve.
Bline, Abigail P et al. “What Is Lost in the Weismann Barrier?.” Journal of developmental biology vol. 8,4 35. 16 Dec. 2020, doi:10.3390/jdb8040035
Brunet, Tyler D P, and W Ford Doolittle. “Multilevel Selection Theory and the Evolutionary Functions of Transposable Elements.” Genome biology and evolution vol. 7,8 2445–57. 6 Aug. 2015, doi:10.1093/gbe/evv152
Futuyma, Douglas J. Evolutionary Biology. W.H. Freeman, 2006.
Gintis, Herbert. “Gene-culture coevolution and the nature of human sociality.” Philosophical transactions of the Royal Society of London. Series B, Biological sciences vol. 366,1566 (2011): 878–88. doi:10.1098/rstb.2010.0310
Heath, Joseph. Following the Rules: Practical Reasoning and Deontic Constraint. Oxford University Press, 2011.
Jablonka, Eva, and Gal Raz. “Transgenerational epigenetic inheritance: prevalence, mechanisms, and implications for the study of heredity and evolution.” The Quarterly review of biology vol. 84,2 (2009): 131–76. doi:10.1086/598822
Kuhn, Steven. “Prisoner’s Dilemma.” Stanford Encyclopedia of Philosophy, Stanford University, 2 Apr. 2019, https://plato.stanford.edu/entries/prisoner-dilemma/.
Kramer, Jos, and Joël Meunier. “Kin and multilevel selection in social evolution: a never-ending controversy?.” F1000Research vol. 5 F1000 Faculty Rev-776. 28 Apr. 2016, doi:10.12688/f1000research.8018.1
Lind, M.I., Spagopoulou, F. Evolutionary consequences of epigenetic inheritance. Heredity 121, 205–209 (2018). https://doi.org/10.1038/s41437-018-0113-y
Niklas, Karl J, and Stuart A Newman. “The many roads to and from multicellularity.” Journal of experimental botany vol. 71,11 (2020): 3247–3253. doi:10.1093/jxb/erz547
Simon, Burton et al. “Towards a general theory of group selection.” Evolution; international journal of organic evolution vol. 67,6 (2013): 1561–72. doi:10.1111/j.1558–5646.2012.01835.
Wilson, E. O., and B. Holldobler. “Eusociality: Origin and Consequences.” Proceedings of the National Academy of Sciences, vol. 102, no. 38, 2005, pp. 13367–13371., https://doi.org/10.1073/pnas.0505858102.
Abbot, Patrick et al. “Inclusive fitness theory and eusociality.” Nature vol. 471,7339 (2011): E1–4; author reply E9–10. doi:10.1038/nature09831
