Risk-dominant Equilibrium in Chicken and Stag-hunt Games with Different Dilemma Strengths

Abstract

Objective: This study investigates how the strength of risk-averting and gamble-intending dilemmas can affect the risk-dominant equilibrium in chicken and stag-hunt games. The focus is on deriving conditions under which the risk-dominant equilibrium can maximize group benefit. Methods: Basic concepts of game theory were used to determine the Nash equilibria of each game.The Harsanyi-Selten theory was applied to determine the risk-dominant equilibrium. By manipulating the parameters related to risk-averting and gamble-intending dilemmas, different game scenarios are sim-ulated to observe the resulting equilibria. Results: The study found that for a given strength of the risk-averting dilemma, the risk-dominant equilibrium in the chicken game continuously shifts towards mutual cooperation as the strength of the gamble-intending dilemma decreases. In the SH game, the degree of cooperation of the risk-dominant equilibrium for a given strength of the gamble-intending dilemma decreases with increasing strength of the risk-averting dilemma and takes the discrete values: 1, 0.5 and 0. The results show the importance of understanding individual risk preferences to predict strategic decisions and equilibrium outcomes in these game settings. Conclusion: The risk-dominant equilibrium in chicken and stag-hunt games depends on the relative strength of the risk-averting and gamble-intending dilemmas. By taking these factors into account, researchers and policy makers can better predict the likely outcomes of strategic interactions in scenarios with conflicting interests and different risk tolerances. The risk-dominant equilibrium can provide reasonable solutions to real-world conflict situations, such as the Iran-Iraq conflict over shared oil and gas resources.

Risk-dominant equilibrium in chicken and stag-hunt games with different dilemma strengths

“…The RDE can provide participants with a reliable focal point. In some cases, the RDE coincides with the PO equilibrium and can improve group benefit [22]. The risk-dominance criterion is fairer than other criteria.…”

“…To select a unique equilibrium in both the CH and SH games, we apply the riskdominance criterion [21,22]. For the CH game, we have…”

“…The risk-dominance criterion [21,22] compares the risk of each equilibrium, which is usually measured by the potential loss a participant could suffer if the opponent deviates. The equilibrium with the lower risk is called the risk-dominant equilibrium (RDE).…”

“…The aim of this study is to solve the dilemma of choosing a unique NE in the QPD. We apply the Situ approach [47] and risk-dominance criterion [21,22] and investigate the effects of the dilemma strength parameters and entanglement.…”

“…In Section 5, we investigate the dilemma of choosing a unique NE in the QPD. Both the Situ [47] and the RDE [22] approaches are used. The influence of the dilemma strength parameters and entanglement is emphasized.…”