A factory is suspected of hiring illegal immigrants as worker.. The authority is

Question

A factory is suspected of hiring illegal immigrants as worker.. The authority is deciding whether to conduct an inspection. If the factory has illegal workers and an inspection takes place, the workers will he discovered. The cost of an inspection to the government is 100. The benefit from the inspection is 500 if illegal workers are found, but 0 if none arc found. The payoff to the authority from conducting an inspection is the benefit minus the cost, while the payoff from not inspecting is 0. For the factory. the payoff from having illegal workers and not getting caught is 200, from not using illegal workers is 0. and from vising illegal workers and getting caught is - 300 A factory must decide whether or not to use illegal workers, and the government must decide whether or not to conduct an inspection. Find all mixed-strategy Nash equilibria. For the game below, find all of the mixed-strategy Nash equilibria. The first payoff in a cell is for player 1. the second payoff is for player 2. and third payoff is for player 3. For the Avranches Gap game in . find the security strategies and security payoffs for General Bradley and G eneral von Kluge. Consider the modified rock-Paper -scissors below. Find a symmetric mioxed-strategy Nash equilibrium.

Explanation / Answer

The game does not have any nash eq. In the three player game we solve in a similar fashion as the 2 player game. Initially we set an option for the alternative picked by player 3 and underline the best options for player 1 and 2 respectively. Say if player 3 chooses to hug, for player 2 to kiss the best alternative is cuddle for player 1 and for player 2 to slap the highest payoff is in choosing poke. Hence likewise we mark the alternatives for player 1 and 2. Next we compare the same order cells in the two matrices to choose the alternative for player 3 with a higher payoff. For instance, when P1=Cuddle, P2=Kiss, the best alternative for P3 is both hug and shove according to the 1X1 cells in both matrices. Similarly we underline for P3. In the end we find that there is no nash eq.

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