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# Consider the game of promotion and sabotage from the lecture. The determinants of a player's performance are

reproduced in the figure below. Recall that the player with the highest performance wins and earns the payoff of 1. If two players are tied for the top spot, each earns 0.5. If three players are tied, each earns 0.33. The payoff is 0 when a player loses.

Suppose the player's initial performance is v1=0 and v2=v3=1. Determine whether the following strategy profile is a Nash equilibrium: (player 1 is negative against player 2, player 2 is negative against player 3, player 3 is negative against player 1) or (neg2,neg3,neg1) for short.

2. Consider the game of promotion and sabotage from the lecture. The determinants of a player’s
performance are reproduced in the figure below. Recall that the player with the highest
performance wins and earns the payoff of 1. If two players are tied for the top spot, each earns
0.5. If three players are tied, each earns 0.33. The payoff is 0 when a player loses. Suppose the player's initial performance is V1=0 and V2=V3=1. Determine whether the following
strategy profile is a Nash equilibrium: (player 1 is negative against player 2, player 2 is negative
against player 3, player 3 is negative against player 1) or (neg2,neg3,neg1) for short. Amount of Positive Amount of Negative
Effort by I Effort Against I

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