Computation Of Efficient Nash Equilibria For Experimental Economic Games

ABSTRACT

Game theory has been used to study a wide variety of human and animal behaviours. 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, dierent equilibria

can have dierent 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 identied and computed the most ecient Nash equilibrium in such

experimental economic games. To achieve this we described and carried out an experiment

on a game that was modelled as a three-player experimental economic game. The results

were recorded and by the best response sets method we identied all the Pure Nash

equilibria and computed the most ecient Nash equilibrium for our experimental economic

game. Using the Brauwer's xed point theorem we veried the existence of mixed Nash

equilibrium in the experimental economic game. The ndings were that the most ecient

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

prots, the payo dominant strategies were played in cooperation to achieve the most

ecient Nash Equilibrium for the experimental economic game. The computation of

most ecient 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.

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