Name required. Mail will not be published required. Game Theory and Evolutionary Biology Game theory is the mathematical analysis for investigating strategies in competitive situations where the outcome for a competitor depends on the choice of action by the other participant s. Google Search. Entries Comments. Hosted by CampusPress. Skip to toolbar Log In Search. This claim, of course, has not gone without comment. In his seminal work Convention , David Lewis developed the idea of sender-receiver games.
Such games have been used to explain how language, and semantic content, can emerge in a community which originally did not possess any language whatsoever. Lewis, , pp. Since the publication of Convention , it is more common to refer to the communicator as the sender and the members of the audience as receivers. The basic idea behind sender-receiver games is the following: Nature selects which state of the world obtains. The person in the role of Sender observes this state of the world correctly identifying it , and sends a signal to the person in the role of Receiver.
The Receiver, upon receipt of this signal, performs a response. If what the Receiver does is the correct response, given the state of the world, then both players receive a payoff of 1; if the Receiver performed an incorrect response, then both players receive a payoff of 0.
Notice that, in this simplified model, no chance of error exists at any stage. The Sender always observes the true state of the world and always sends the signal he intended to send. Likewise, the Receiver always receives the signal sent by the Sender i. We shall see later why larger sender-receiver games are increasingly difficult to analyse. Since we are considering the case where there is only a single responder, the second requirement is otiose.
It is, as Lewis notes, a function from the set of states of the world into the set of signals. This means that it is possible that a sender may send the same signal in two different states of the world.
Such a strategy makes no sense, from a rational point of view, because the receiver would not get enough information to be able to identify the correct response for the state of the world. However, we do not exclude these strategies from consideration because they are logically possible strategies. How many sender strategies are there? This means there are four possible sender strategies. What is a strategy for a receiver? As in the case of the sender, we allow the receiver to perform the same response for more than one signal.
These receiver strategies are:. All other possible combinations of strategies result in the players failing to coordinate. What if the roles of Sender and Receiver are not permanently assigned to individuals? That is, what if nature flips a coin and assigns one player to the role of Sender and the other player to the role of Receiver, and then has them play the game?
It makes a difference whether one considers the roles of Sender and Receiver to be permanently assigned or not. If the roles are assigned at random, there are four signaling systems amongst two players [ 12 ] :.
Signaling systems 3 and 4 are curious. System 3 is a case where, for example, I speak in French but listen in German, and you speak German but listen in French. System 4 swaps French and German for both you and me.
Notice that in systems 3 and 4 the players are able to correctly coordinate the response with the state of the world regardless of who gets assigned the role of Sender or Receiver.
The problem, of course, with signaling systems 3 and 4 is that neither Player 1 nor Player 2 would do well when pitted against a clone of himself. They are cases where the signaling system would not work in a population of players who are pairwise randomly assigned to play the sender-receiver game.
In fact, it is straightforward to show that the strategies Sender 2, Receiver 2 and Sender 3, Receiver 3 are the only evolutionarily stable strategies see Skyrms , 89— As a first approach to the dynamics of sender-receiver games, let us restrict attention to the four strategies Sender 1, Receiver 1 , Sender 2, Receiver 2 , Sender 3, Receiver 3 , and Sender 4, Receiver 4.
Figure 16 illustrates the state space under the continuous replicator dynamics for the sender-receiver game consisting of two states of the world, two signals, and two responses, where players are restricted to using one of the previous four strategies.
One can see that evolution leads the population in almost all cases [ 13 ] to converge to one of the two signaling systems. Figure 17 illustrates the outcome of one run of the replicator dynamics for a single population model where all sixteen possible strategies are represented. We see that eventually the population, for this particular set of initial conditions, converges to one of the pure Lewisian signalling systems identified above.
Figure The evolution of a signalling system under the replicator dynamics. When the number of states of the world, the number of signals, and the number of actions increase from 2, the situation rapidly becomes much more complex.
Given this, one might think that it would prove difficult for evolution to settle upon an optimal signalling system. Such an intuition is correct. Hofbauer and Hutteger show that, quite often, the replicator dynamics will converge to a suboptimal outcome in signalling games.
In these suboptimal outcomes, a pooling or partial pooling equilibrium will emerge. A pooling equilibrium occurs when the Sender uses the same signal regardless of the state of the world.
A partial pooling equilibrium occurs when the Sender is capable of differentiating between some states of the world but not others. Furthermore, suppose that the Receiver performs action 1 upon receipt of signal 1, and action 2 upon receipt of signals 2 and 3. If all states of the world are equiprobable, this is a partial pooling equilibrium. Given that the Sender does not differentiate states of the world 2 and 3, the Receiver cannot improve his payoffs by responding differently to signal 2.
Given the particular response behaviour of the Receiver, the Sender cannot improve her payoffs by attempting to differentiate states of the world 2 and 3. As noted previously, evolutionary game theoretic models may often be given both a biological and a cultural evolutionary interpretation. In many cases, fitness in cultural evolutionary interpretations of evolutionary game theoretic models directly measures some objective quantity of which it can be safely assumed that 1 individuals always want more rather than less and 2 interpersonal comparisons are meaningful.
Depending on the particular problem modeled, money, slices of cake, or amount of land would be appropriate cultural evolutionary interpretations of fitness. Requiring that fitness in cultural evolutionary game theoretic models conform to this interpretative constraint severely limits the kinds of problems that one can address.
A more useful cultural evolutionary framework would provide a more general theory which did not require that individual fitness be a linear or strictly increasing function of the amount of some real quantity, like amount of food. Consequently, the utility theory used in traditional game theory cannot simply be carried over to evolutionary game theory.
Another question facing evolutionary game theoretic explanations of social phenomena concerns the kind of explanation it seeks to give. Depending on the type of explanation it seeks to provide, are evolutionary game theoretic explanations of social phenomena irrelevant or mere vehicles for the promulgation of pre-existing values and biases? To understand this question, recognize that one must ask whether evolutionary game theoretic explanations target the etiology of the phenomenon in question, the persistence of the phenomenon, or various aspects of the normativity attached to the phenomenon.
The latter two questions seem deeply connected, for population members typically enforce social behaviors and rules having normative force by sanctions placed on those failing to comply with the relevant norm; and the presence of sanctions, if suitably strong, explains the persistence of the norm. If one wishes to explain how some currently existing social phenomenon came to be, it is unclear why approaching it from the point of view of evolutionary game theory would be particularily illuminating.
The etiology of any phenomenon is a unique historical event and, as such, can only be discovered empirically, relying on the work of sociologists, anthropologists, archaeologists, and the like. Although an evolutionary game theoretic model may exclude certain historical sequences as possible histories since one may be able to show that the cultural evolutionary dynamics preclude one sequence from generating the phenomenon in question , it seems unlikely that an evolutionary game theoretic model would indicate a unique historical sequence suffices to bring about the phenomenon.
An empirical inquiry would then still need to be conducted to rule out the extraneous historical sequences admitted by the model, which raises the question of what, if anything, was gained by the construction of an evolutionary game theoretic model in the intermediate stage. Moreover, even if an evolutionary game theoretic model indicated that a single historical sequence was capable of producing a given social phenomenon, there remains the important question of why we ought to take this result seriously.
One may point out that since nearly any result can be produced by a model by suitable adjusting of the dynamics and initial conditions, all that the evolutionary game theorist has done is provide one such model. Additional work needs to be done to show that the underlying assumptions of the model both the cultural evolutionary dynamics and the initial conditions are empirically supported. Again, one may wonder what has been gained by the evolutionary model—would it not have been just as easy to determine the cultural dynamics and initial conditions beforehand, constructing the model afterwards?
If so, it would seem that the contributions made by evolutionary game theory in this context simply are a proper part of the parent social science—sociology, anthropology, economics, and so on. If so, then there is nothing particular about evolutionary game theory employed in the explanation, and this means that, contrary to appearances, evolutionary game theory is really irrelevant to the given explanation.
If evolutionary game theoretic models do not explain the etiology of a social phenomenon, presumably they explain the persistence of the phenomenon or the normativity attached to it.
Yet we rarely need an evolutionary game theoretic model to identify a particular social phenomenon as stable or persistent as that can be done by observation of present conditions and examination of the historical records; hence the charge of irrelevancy is raised again.
Moreover, most of the evolutionary game theoretic models developed to date have provided the crudest approximations of the real cultural dynamics driving the social phenomenon in question. One may well wonder why, in these cases, we should take seriously the stability analysis given by the model; answering this question would require one engage in an empirical study as previously discussed, ultimately leading to the charge of irrelevance again.
That is, an evolutionary game theoretic model shows how some phenomenon could possibly be generated by an underlying dynamical process of interacting, boundedly rational agents. Although this is certainly the case, one might wonder whether this subtly shifts the explanatory target. This suggests that evolutionary game theoretic explanations of social phenomena are, even in the best cases, incomplete.
After all, since any argument whose conclusion is a normative statement must have at least one normative statement in the premises, any evolutionary game theoretic argument purporting to show how certain norms acquire normative force must contain—at least implicitly—a normative statement in the premises.
Consequently, this application of evolutionary game theory does not provide a neutral analysis of the norm in question, but merely acts as a vehicle for advancing particular values, namely those smuggled in the premises. This criticism seems less serious than the charge of irrelevancy.
The theory already contains, in its core, a proper subtheory having normative content—namely a theory of rational choice in which boundedly rational agents act in order to maximize, as best as they can, their own self-interest. One may challenge the suitability of this as a foundation for the normative content of certain claims, but this is a different criticism from the above charge.
Although cultural evolutionary game theoretic models do act as vehicles for promulgating certain values, they wear those minimal value commitments on their sleeve. Historical Development 2. Two Approaches to Evolutionary Game Theory 2. Dynamics, Stability, and Rational Outcomes 4. Why Evolutionary Game Theory? Applications of Evolutionary Game Theory 5. Philosophical Problems of Evolutionary Game Theory 6.
Historical Development Evolutionary game theory was first developed by R. Rock-Scissors-Paper with a feeble twin. Figure The evolution of signaling systems. Bibliography Akin, Ethan Alexander, J. McKenzie Alexander, Jason and Brian Skyrms Axelrod, R.
The Evolution of Cooperation. New York: Basic Books. Barrett, Jeffrey A. Bicchieri, Cristina Binmore, Ken and Samuelson, Larry Boehm, C. Brown, George W. Chalub, F. Pacheco Clemens, Christiane and Thomas Riechmann Danielson, P. Enquist, Magnus and Stefano Ghirlanda Enquist, M. Fishman, Michael A. Fisher, R. Fletcher, Jeffrey A. Gintis, Herbert Hargreaves Heap, Shaun P.
Harms, William Harms, William and Brian Skyrms Harsanyi, J. Hauert, Christoph Nowak, and Michael Doebeli Hausken, Kjell, and Jack Hirshleifer Hofbauer, Josef and Simon Huttegger Hofbauer, Josef, P. Schuster and K. Sigmund Journal of Theoretical Biology , — Hofbauer, Josef P. Sandholm The further evolution of cooperation. Science , The evolution of cooperation. Evolutionary stable strategies and game dynamics.
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Introduction to Population Demographics. Population Dynamics of Mutualism. Population Ecology Introduction. Population Limiting Factors. The Breeder's Equation. Global Atmospheric Change and Animal Populations. Semelparity and Iteroparity. Causes and Consequences of Dispersal in Plants and Animals. Disease Ecology. Survivorship Curves.
The Population Dynamics of Vector-borne Diseases. Citation: Cowden, C. Nature Education Knowledge 3 10 If natural selection is survival of the fittest, why isn't everything a competition? Cooperation and competition have a fitness face off in game theory. Aa Aa Aa. Evolutionary Stable Strategies.
In some populations, all individuals may have the same strategy phenotype. Such a strategy is said to be an evolutionary stable strategy or ESS if that strategy cannot be replaced, or invaded by any other strategy through natural selection 4,5.
Formally, and ESS must satisfy two conditions 4 : 1 an individual employing strategy A must do better against another individual employing strategy A than any other strategy; and 2 should a new strategy evolve A' that does equally well against strategy A, for A to be an ESS, an individual employing strategy A must do better against an individual employing strategy A' than an individual employing strategy A'. A hawk is aggressive and initiates a combative interaction when confronted; alternatively, the dove is passive and avoids combative interactions.
A hawk may encounter another hawk, or a dove; likewise, a dove may encounter another dove, or a hawk. If the two individuals adopt a dove strategy, the resources are partitioned equally. If a dove encounters a hawk, the hawk acquires the totality of the resource, while the dove receives none. Lastly, if a hawk encounters another hawk, the resources are partitioned equally; however, there is a cost incurred by each hawk due to the aggressive interaction.
A population of doves may be invaded by a hawk, and the hawk strategy will displace the dove strategy Fig. If the cost of conflict is greater than the reward, then neither the hawk nor the dove strategy satisfies the conditions of ESS as a pure strategy.
Complex Interactions. The principles of game theory provide a theoretical framework for understanding the evolution of biological interactions. Evolutionary game theory applies to organisms that interact repeatedly, both within a generation and over evolutionary relevant timescales. In special cases, evolutionary stable strategies emerge in which a particular strategy is adopted by all members of a population and alternative strategies mutant phenotypes cannot invade and displace the ESS.
The flexibility of game theory allows for the testing of complex mixed strategies and incorporating reward and punishment in evolutionary strategies. Importantly, game theory demonstrates the evolution of cooperation and altruism ESSs is consistent with evolution through natural selection. References and Recommended Reading 1 Smith, J. Evolution and the Theory of Games. Cambridge University Press, Share Cancel.
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