Reference no: EM132412715

Two male octopuses, an older male and a younger male, are competing for access to female octopuses. The older male has 2 strategies available to him. He can defend a territory and make sexy signals to attract multiple females and form a harem (harem strategy). Or he can convince one female to mate, then follow her around for as long as she's fertile (~10 days), mating regularly, and chasing away any other octopuses who approach (mate- guard strategy). The young male has 3 strategies available to him: the harem strategy and the mate-guard strategy (same as the older male's strategies), plus a "sneaker" strategy. In the sneaker strategy, he pretends to be a female by changing his coloration to match a female, then hides behind a rock near a mating pair and when the male isn't watching, reaches out his mating arm to pass sperm to the female (yes, this is a real strategy used by some octopuses); males do not pay any cost for playing the sneaker strategy. Playing the harem strategy can earn 45 FU for players of either age, but signaling and territorial defense is expensive, so playing this strategy always costs 18 FU for older males and 32 FU for younger males (regardless of the outcome of their interactions with other males). The guarding strategy can earn 25 FU for players of either age, but defending the female always costs 10 FU for the older male and 17 FU for the younger male (regardless of the outcome of their interactions with other males). When both males try the harem strategy at the same time, the older male always wins the matings and gains the fitness benefit. When both males play the mate-guard strategy at the same time, the older male wins the matings 90% of the time. When a harem male competes against a mate-guard male, the harem male wins the matings 60% of the time, regardless of his age (they each gain the benefits and pay the costs of their respective strategies). When a sneaker male competes against a guarding male, the sneaker gets chased away and is unsuccessful at sneaking any fertilizations. When a sneaker competes against a harem male, he is able to fertilize 20% of the eggs and thus gain 20% of the 45 FU; the harem male gets the rest of the FU.

(a) On the backside of this page (or an attached page), draw a payoff matrix for this game (show how you calculate each payoff for full credit!), and find the ESS

(b) Is this game symmetric or asymmetric?

(c) Describe the ESS, if any (include the same terms in your description as you did in problems 1-4)