Cooperation risk and Nash equilibrium: Quantitative description for realistic players

The emergence of cooperation figures among the main goal of game theory in competitive-cooperative environments. Potential games have long been hinted as viable alternatives to study realistic player behavior. Here, we expand the potential games approach by taking into account the inherent risks of...

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Bibliographic Details
Published in:Physica A 2019-02, Vol.515, p.102-111
Main Authors: Nakamura, G.M., Contesini, G.S., Martinez, A.S.
Format: Article
Language:English
Subjects:
Complex system
Game theory
Phase transitions
Potential games
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Summary:The emergence of cooperation figures among the main goal of game theory in competitive-cooperative environments. Potential games have long been hinted as viable alternatives to study realistic player behavior. Here, we expand the potential games approach by taking into account the inherent risks of cooperation. We show the Public Goods game reduce to a Hamiltonian with one-body operators, with the correct Nash Equilibrium as the ground state. The inclusion of punishments to the Public Goods game reduces cooperation risks, creating two-body interactions with a rich phase diagram, in which phase transitions segregates cooperative from competitive regimes. •Mathematical description of cooperation risk to restore Nash equilibrium in potential games.•First- and second-order phase transitions between cooperative and other behaviors.•Punishments and cooperation risk in public goods games with algebraic operators.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2018.09.194