The Minority of Three-Game: An Experimental and Theoretical Analysis

Chmura, Thorsten; Güth, Werner

doi:10.3390/g2030333

Cited by 21 publications

(21 citation statements)

References 21 publications

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“…This result conrms previous ndingsobtained from analyzing choice data in previous minority games experiments (Chmura et al, 2010). Hence, we can conclude that the absence of evidence compatible with the mixed strategy equilibrium does not derive from players' imperfect ability to randomize but from players intentionally not pursuing this type of strategy.…”

Section: Discussionsupporting

confidence: 91%

“…Hence, the mixed strategy equilibrium solution is unsupported by the results of our analysis: this nding conrms the results in Chmura et al (2010) obtained by considering choice data. We can hence state that behaviors incompatible with the mixed strategy equilibrium do not derive from players' imperfect ability to randomize, but from players not intentionally pursuing this type of strategy.…”

supporting

confidence: 90%

“…Belief learning models on the contrary have low predictive success, which is line with the fact that participants mainly collect information about past payos. Chmura et al (2010) conclude that the observed heterogeneity in players' behavior in games where multiple equivalent equilibria are present must be ascribed to the structure of individuals' preferences rather than to their inability to calculate mixed equilibria. Finally, Liu et al (2010) study minority game properties by comparing behavior in the game played by humans and by sh, and discover several behavioral similarities between the two species.…”

Section: Literature Reviewmentioning

confidence: 89%

“…Finally, the path of play shows evidence of mutual adaptation between players' strategies over time. Chmura et al (2010) test the extent to which subjects conform to the symmetric mixed strategy equilibrium in a minority game, by implementing incentives that allow subjects to pick strategies randomly. Their results show that only 25% of their experimental subjects decide to choose according to a coin toss, while the majority implement a decision rule that can be adequately described by a reinforcement learning model.…”

Section: Literature Reviewmentioning

confidence: 99%

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The Minority Game Unpacked: Coordination and Competition in a Team-Based Experiment

Devetag

Pancotto

Brenner³

2011

SSRN Journal

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In minority games, players in a group must decide at each round which of two available options to choose, knowing that only subjects who picked the minority option obtain a positive reward. Previous experiments on the minority and similar congestion games have shown that players interacting repeatedly are remarkably able to coordinate eciently, despite not conforming to Nash equilibrium behavior. We conduct an experiment on a minority-of-three game in which each player is a team composed by three subjects. Each team can freely discuss its strategies in the game and decisions must be made via a majority rule. Team discussions are recorded and their content analyzed to detect evidence of strategy co-evolution among teams Philipps University Marburg, Germany 1 playing together. Our main results of team discussion analysis show no evidence supporting the mixed strategy Nash equilibrium solution, and support a low-rationality, backward-looking approach to model behavior in the game, more consistent with reinforcement learning models than with belief-based models. Showing level-2 rationality (i.e., reasoning about others' beliefs) is positively and signicantly correlated with higher than average earnings in the game, showing that a mildly sophisticated approach pays o. In addition, teams that are more successful tend to become more egocentric over time, paying more attention to their own past successes than to the behavior of other teams. Finally, we nd evidence of mutual adaptation over time, as teams that are more strategic (i.e., they pay more attention to other teams' moves)induce competing teams to be more egocentric instead. Our results contribute to the understanding of coordination dynamics resting on heterogeneity and co-evolution of decision rules rather than on conformity to equilibrium behavior. In addition, they provide support at the decision process level to the validity of modeling behavior using low-rationality reinforcement learning models.JEL codes: C72, C91, C92

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Section: Discussionsupporting

confidence: 91%

supporting

confidence: 90%

Section: Literature Reviewmentioning

confidence: 89%

Section: Literature Reviewmentioning

confidence: 99%

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The Minority Game Unpacked: Coordination and Competition in a Team-Based Experiment

Devetag

Pancotto

Brenner³

2011

SSRN Journal

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show abstract

“…9 collect information about past payos. Chmura et al (2010) conclude that the observed heterogeneity in players' behavior in games where multiple equivalent equilibria are present must be ascribed to the structure of individuals' preferences rather than to their inability to calculate mixed equilibria. Finally, Liu et al (2010) study minority game properties by comparing behavior in the game played by humans and by sh, and discover several behavioral similarities between the two species.…”

mentioning

confidence: 89%

The Minority Game Unpacked: Coordination and Competition in a Team-Based Experiment

Devetag¹,

Pancotto

Brenner

2011

SSRN Journal

View full text Add to dashboard Cite

In minority games, players in a group must decide at each round which of two available options to choose, knowing that only subjects who picked the minority option obtain a positive reward. Previous experiments on the minority and similar congestion games have shown that players interacting repeatedly are remarkably able to coordinate eciently, despite not conforming to Nash equilibrium behavior. We conduct an experiment on a Minority-of-three game in which each player is a team composed by three subjects. Each team can freely discuss its strategies in the game and decisions must be adopted through a majority rule. Team discussions are recorded and their content analyzed to detect evidence of strategy co-evolution between teams playing together. Our main results of group discussion analysis show no evidence non conformity to Nash at the choice data level does not derive from imperfect ability to randomize, but by players intentionally not pursuing this type of strategy. In addition, teams that are more successful tend to be more self-centered over time, paying more attention to their own past successful strategies than to the behavior of other teams. Moreover, we nd evidence of mutual adaptation between players' strategies, as teams that are more sophisticated (i.e., they pay more attention to other teams' moves) tend, on average, to induce other teams to be less sophisticated and more self-centered. Our results contribute to the understanding of coordination dynamics resting on heterogeneity and co-evolution of decision rules rather than on conformity to equilibrium behavior, both at the aggregate and at the individual level.JEL codes: C72, C91, C92

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To be at the tail of the lions or the head of the foxes?

Avrahami

Ezer

Güth

et al. 2019

Behavioral Decision Making

Self Cite

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Agents seeking an opportunity for profit often have to compete with others who pursue the same opportunity. When having to choose between a number of opportunities differing in their value and if individuals differ in their chances of outperforming others, the choice can be cognitively and emotionally demanding. We explore choice between opportunities using stylized Lions–Foxes games. In such a game, each of three players, with different odds of beating others, has to choose one of two contests that offer different rewards. After game theoretically analyzing the games, which we have experimentally employed, we report four experiments that vary in choice elicitation (repeated play or strategy method), in players' matching (random strangers or partners) and in rewards. Regarding contest choices, we found the choice of the higher value (and seemingly more prestigious) contest to be positively related to winning odds, contrary to what four out of the five (mixed, partially mixed, or pure) equilibria predict. Participants started out rather optimistic, with a large majority choosing the higher value option, but with experience, they approached the only viable of two pure strategy equilibria. Still, mixing continued via reacting to past play and outcome, apparently balancing dissatisfaction from choosing either contest.

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The Minority of Three-Game: An Experimental and Theoretical Analysis

Cited by 21 publications

References 21 publications

The Minority Game Unpacked: Coordination and Competition in a Team-Based Experiment

The Minority Game Unpacked: Coordination and Competition in a Team-Based Experiment

The Minority Game Unpacked: Coordination and Competition in a Team-Based Experiment

To be at the tail of the lions or the head of the foxes?

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