A Bayesian model of quasi-magical thinking can explain observed cooperation in the public good game

Masel, Joanna

doi:10.1016/j.jebo.2005.07.003

Cited by 28 publications

(20 citation statements)

References 36 publications

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“…While players are best reply reasoners when their beliefs about the action of the other is fixed (in line with the ratifiability assumption), they are not in presence of uncertainty. xiii Masel (2007) formalises the idea of ADB in a 'Bayesian model of quasi-magical thinking', and shows that in public good games a positive correlation between the players' contributions and their beliefs about the strategy of others can explain cooperative behaviours. Hammond (2009) also defended ADB as a case of 'rational folly', since although players know that their actions cannot directly influence the actions of others, they could be better off if they actually hold that belief: it would therefore be rational for them to hold irrational and false beliefs (see Lecouteux, 2015, propositions 11 and 12, for an evolutionary justification of 'rationally irrational' behaviours).…”

Section: Simulation Ratifiability and Action-dependent Beliefsmentioning

confidence: 96%

Mindreading and endogenous beliefs in games

Larrouy

Lecouteux

2017

Journal of Economic Methodology

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Section: Simulation Ratifiability and Action-dependent Beliefsmentioning

confidence: 96%

Mindreading and endogenous beliefs in games

Larrouy

Lecouteux

2017

Journal of Economic Methodology

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“…Although this characterization behavior is simple, it can allow for a rich analysis as a form of minimal cognition (Beer 2003) and we can associate a cognitive cost for this extra decision-making ability (Kaznatcheev 2010). Or push this genotype to behavior map even further (Kaznatcheev, Montrey, and Shultz 2014) by having evolving agents act rationally on their evolved perceptions of the game payoffs and (potentially-biased) estimates of other's probability to cooperate (for this direction, see also Masel (2007)).…”

Section: Fitness For Individuals and Reductive Gamesmentioning

confidence: 99%

Two conceptions of evolutionary games: reductive vs effective

Kaznatcheev

2017

Preprint

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Evolutionary game theory (EGT) was born from economic game theory through a series of analogies. Given this heuristic genealogy, a number of central objects of the theory (like strategies, players, and games) have not been carefully defined or interpreted. A specific interpretation of these terms becomes important as EGT sees more applications to understanding experiments in microscopic systems typical of oncology and microbiology. In this essay, I provide two interpretations of the central objects of games theory: one that leads to reductive games and the other to effective games. These interpretation are based on the difference between views of fitness as a property of individuals versus fitness as a summary statistic of (sub)populations. Reductive games are typical of theoretical work like agent-based models. But effective games usually correspond more closely to experimental work. However, confusing reductive games for effective games or vice-versa can lead to divergent results, especially in spatially structured populations. As such, I propose that we treat this distinction carefully in future work at the interface of EGT and experiment.In my views of game theory, I largely follow Rubinstein (2012): game theory is a set of fables. A collection of heuristic models that helps us structure how we make sense of and communicate about the world. Evolutionary game theory (EGT) was born of classic game theory through a series of analogies. Given this heuristic genealogy of the field, it is usually alright to not worry too much about what exactly terms like strategy, player, or game really mean or refer to. I am usually happy to leave these terms ambiguous so that they can motivate different readers to have different interpretations and subsequently push for different models of different experiments. I think it is essential for heuristic theories to foster this diverse creativity: anything goes.However, not everyone would agree with Rubinstein and me; some people think that EGT isn't "just" heuristics. EGT is also directly empirically useful for questions in both mathematical oncology and the evolution of microorganisms. Microscopic experimental systems in which EGT has been use- (Kaznatcheev et al. 2017b). But when we actually start doing experiments like these, it is no longer acceptable to be willy-nilly with fundamental objects of the theory: strategies, players, and games. The biggest culprit is the player. In particular, I think that a lot of confusion stems from saying that "cells are players".In classical game theory, the concepts of player, strategy, and game are intertwined but relatively straightforward. Players use a rational decision process to select strategies which are then mapped by the rules of the game to payoffsthe utility given to the players. Or, as I say more awkwardly in the first column of table 1: utility is given to a player based on its strategy which results from a rational decision process carried out by the player. All of this is summarized as the game. But, how does this classic pict...

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“…42 Specifically, because in these models all Kantians or rule utilitarians evaluate strategies in the same way, any heterogeneity in nonstandard behavior is driven completely by asymmetry in the physical aspects of the game (e.g., variations in the cost of voting). In contrast, even in symmetric games, our model captures heterogeneity in behavior (e.g., in the sets of PD games that different players choose to cooperate in).43 Additional models in which players' beliefs about opponent play may be biased includeOrbell and Dawes (1991),Bernheim and Thomadsen (2005),Masel (2007),Capraro and Halpern (2015), alNowaihi and Dhami (2015).44 In addition, our behavioral model introduces the possibility of equilibrium multiplicity even in the PD, depending on F . It is then the axioms that rule out models with multiplicity, again showing that the second concern can also be addressed axiomatically.…”

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confidence: 99%

Magical thinking: A representation result

Daley

Sadowski

2017

Theoretical Economics

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This paper suggests a novel way to import the approach of axiomatic theories of individual choice into strategic settings and demonstrates the benefits of this approach. We propose both a tractable behavioral model as well as axioms applied to the behavior of the collection of players, focusing first on prisoners' dilemma games. A representation theorem establishes these axioms as the precise behavioral content of the model, and that the model's parameters are (essentially) uniquely identified from behavior. The behavioral model features magical thinking : players behave as if their expectations about their opponents' behavior vary with their own choices. The model provides a unified view of documented behavior in a range of often studied games, such as the prisoners' dilemma, the battle of the sexes, hawk-dove, and the stag hunt, and also generates novel predictions across games.Earlier working versions circulated under the titles "Foundations for cooperation in the prisoners' dilemma" and "A strategic model of magical thinking: Axioms and analysis." We are grateful to a co-editor and three anonymous referees for helpful comments and suggestions. We also thank

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A Bayesian model of quasi-magical thinking can explain observed cooperation in the public good game

Cited by 28 publications

References 36 publications

Mindreading and endogenous beliefs in games

Mindreading and endogenous beliefs in games

Two conceptions of evolutionary games: reductive vs effective

Magical thinking: A representation result

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