Game Theory Question Diluted Happiness: Consider a relationship between a barten
ID: 457700 • Letter: G
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Game Theory Question
Diluted Happiness: Consider a relationship between a bartender and a cus tomer. The bartender serves bourbon to the customer and chooses x E [0, 1 which is the proportion of bourbon in the drink served, while 1-x is the pro- portion of water. The cost of supplying such a drink (standard 4-ounce glass is cx, where c 0. The customer, without knowing x, decides on whether or not to buy the drink at the market price p. If he buys the drink his payoff is vx p, and the bartender's payoff is p cx. Assume that v c and all pay offs are common knowledge. If the customer does not buy the drink he gets 0 and the bartender gets -cx. Because the customer has some experience, once the drink is bought and he tastes it, he learns the value of x, but this is only after he pays for the drink.Explanation / Answer
In game theory, the Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his or her own strategy.[1] If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitutes a Nash equilibrium. The reality of the Nash equilibrium of a game can be tested using experimental economics methods.
Stated simply, Amy and Will are in Nash equilibrium if Amy is making the best decision she can, taking into account Will's decision while Will's decision remains unchanged, and Will is making the best decision he can, taking into account Amy's decision while Amy's decision remains unchanged. Likewise, a group of players are in Nash equilibrium if each one is making the best decision possible, taking into account the decisions of the others in the game as long as the other party's decision remains unchanged.
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