Question

5. (Nash) This is a two-person complete information game called "Pigs in a Box". The story is that there are two pigs, one strong and one weak, in a box. They are both trying to maximize net caloric intake. 100 calories of food appear at the dispenser when a pig pushes the lever. Pushing the lever takes 10 calories of effort. Each pig has to decide whether to push the lever or wait by the dispenser. If both push the lever, both pigs lose 10 calories of effort and the strong pig gets all the food at the dispenser. If both wait at the dispenser, no- one gets food. If the weak pig pushes the lever and the strong pig waits at the dispenser, the weak pig loses 10 calories and the strong pig gets all the food. And if the strong pig pushe:s the lever and the weak pig waits by the dispenser, the strong pig loses 10 calories, but gets 4 of the food, while the weak pig get5% of the food. The payoff matrix is: Strong Pig's Strategy Wait by Dispenser Strong 100: Weak -10 Weak Pig's Strategy Push lever Wait by Dispenser Strong +90: Weak -10 Strong +15: Weak +75 | Strong 0: Weak 0 Identify all Nash equilibria of this game (there might be none, one, or two).

Answer 1

A strategy is said to be dominant if, the pay off the strategy is largest among the available strategy to this players regardless of strategy chosen by other players. Hence, it can be said that a strategy is dominant if it is always superior, compare to any other strategy, for any profile of other player’s action.

Since the Nash equilibrium occurs when every player wants to choose the best possible strategy, given the strategies of another player. Once the Nash equilibrium is reached, there is no incentive to change the strategy by the both players.

As it can be table that dominant strategy for Weak pig's strategy is push lever if strong pig's strategy choose push lever.

Similarly if strong pig's strategy choose push wait by dispenser, the dominant strategy for Weak pig's strategy is push lever.

As it can be table that there is no dominant strategy for strong pig's strategy because he has equal pay off if weak pig's choose push lever..

Similarly if weak pig's strategy choose push wait by dispenser, the dominant strategy for strong pig's strategy is push lever.

Since there is no nash equilibrium because in no cell both player have dominant strategy in any strategy.

For nash equilibrium there should be dominant strategy by the both players.