Question

? EXERCISE 18.1 (Hermaphroditic fish) Members of some species of hermaphroditic fish choose, in each mating encounter, whether to play the role of a male or a female. Each fish has a preferred role, which uses up fewer resources and hence allows more future mating. A fish obtains a payoff of H if it mates in its preferred role and L if it mates in the other role, where H L (Payoffs are measured in terms of number of offspring, which fish are evolved to maximize.) Consider an encounter between two fish whose preferred rolesare the same. Each fish has two possible actions: mate in either role or insist on its preferred role. If both fish offer to mate in either role, the roles are assigned randomly, and each fish's payoff is (H +L) (the average of H and L). If each fish insists on its preferred role, the fish do not mate; each goes off in search of another partner, and obtains the payoff S The higher the chance of meeting another partner, the larger is S. Formulate this situation as a strategic game and determine the range of values of S, for any given values of H and L, for which the game differs from the Prisoner's Dilemma only in the names of the actions

Answer 1

"The question describes the following ""Normal form game"": In the prisoner�s dilemma, each player has a dominant strategy, but the outcome from each player individual�s dominated strategy dominates the outcome from each playing individual�s dominant strategy. For the above game to fit the description, the following 3 inequalities must hold: (i) H > 1/2 (H + L) (ii) S > L (iii) 1/2 (H + L) > S \r\n Inequality (i) is implied by H > L, i.e., it is satisfied by any value of S. Hence the fish game matches the prisoner�s dilemma if and only if S elementof (L, 1/2 (H + L))."