Abstract
Inspired by Shalev’s model of loss aversion, we investigate the effect of loss aversion on a bimatrix game where the payoffs in the bimatrix game are characterized by triangular fuzzy variables. First, we define three solution concepts of credibilistic loss aversion Nash equilibria, and their existence theorems are presented. Then, three sufficient and necessary conditions are given to find the credibilistic loss aversion Nash equilibria. Moreover, the relationship among the three credibilistic loss aversion Nash equilibria is discussed in detail. Finally, for2×2bimatix game with triangular fuzzy payoffs, we investigate the effect of loss aversion coefficients and confidence levels on the three credibilistic loss aversion Nash equilibria. It is found that an increase of loss aversion levels of a player leads to a decrease of his/her own payoff. We also find that the equilibrium utilities of players are decreasing (increasing) as their own confidence levels when players employ the optimistic (pessimistic) value criterion.
Highlights
Since established by von Neumann and Morgenstern (1944), game theory has been applied to modeling strategic interactions for decision problem in many fields, such as economics, political science, and psychology
Langsha Group develops its direct selling business in 2017; it cannot be exactly predicted whether Langsha Group can benefit from the direct selling because of the uncertainty of the consumer demand and the investment cost in direct selling business. To deal with such situation faced by Langsha Group, this paper investigates the impact of loss aversion on equilibrium strategies in bimatrix games with fuzzy payoffs
We extend the analysis of bimatrix games with fuzzy payoffs to incorporate loss aversion
Summary
Since established by von Neumann and Morgenstern (1944), game theory has been applied to modeling strategic interactions for decision problem in many fields, such as economics, political science, and psychology. Since Shalev’s model of loss aversion has received attention in the field of game theory based on the assumption that the payoffs are common knowledge to two players [34,35,36,37,38]. To deal with such situation faced by Langsha Group, this paper investigates the impact of loss aversion on equilibrium strategies in bimatrix games with fuzzy payoffs. We extend the analysis of bimatrix games with fuzzy payoffs to incorporate loss aversion. By means of 2×2 bimatrix game with triangular fuzzy payoffs, we investigate the effect loss aversion coefficients and confidence levels on the three credibilistic loss aversion Nash equilibria.
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