Computation of efficient nash equilibria for experimental economic games

Abstract

Game theory has been used to study a wide variety of human and animal behaviors. It looks for states of equilibrium, sometimes called solutions. Nash equilibrium is the central solution concept with diverse applications for most games in game theory. However some games have no Nash equilibrium, others have only one Nash equilibrium and the rest have multiple Nash equilibria. For games with multiple equilibria, different equilibria can have different rewards for the players thus causing a challenge on their choice of strategies. In this study, to solve the problems associated with existence of multiple equilibria in games, we identified and computed the most efficient Nash equilibrium in such experimental economic games. To achieve this we described and carried out an experiment on a game that was modeled as a three-player experimental economic game. The results were recorded and by the best response sets method we identified all the Pure Nash equilibria and computed the most efficient Nash equilibrium for our experimental economic game. Using the Brauwer's fixed point theorem we verified the existence of mixed Nash equilibrium in the experimental economic game. The findings were that the most efficient equilibrium varied from one player to the other. An individual whose aim was to minimize risks played the risk dominant strategies whereas for those aiming to maximize their profits, the payoff dominant strategies were played in cooperation to achieve the most efficient Nash Equilibrium for the experimental economic game. The computation of most efficient Nash Equilibrium in games can be applied to most situations in competitive Economic environment that are faced with multiple choices on which strategy is optimal.