Problem 3: (The game of \"chicken\") Two cars are driving at each other at great

Question

Problem 3: (The game of "chicken") Two cars are driving at each other at great speeds. If nobody changes directions, i Seconds they wll collide and die a gruesome death, yielding payofs of-100 for both players. At every second they have to (simultaneously) decide whether to continue or not (i.e. there are 3 periods to this game). Payoffs are as follows: If both players choose continue for each of the three periods, then they get -100. If at any period one player choses "not continue" and the other chooses "continue" the player that chose not to continue gets 0 and the other gets 100. If at smepoint both simultaneously choose not to continue they both get 0. True or False: There is an SPNE where player 1 choses to continue at each period and player 2 choses to continue at period 1 and 2 but choses to not continue in period 3 True or False: There is an SPNE were both players choose to not continue at every node True or False: Any equilibrium has the property that one of the players chooses not to continue, but this only happens in the last period (as in the movies!) Problem 4: Solve all NE of the centipede game. Are there NE that are not SPNE? Are there NE where one of the players decides to go forward at the first node?

Explanation / Answer

ans 1 false

ans 2 true

ans 3 false

problem 4: In game theory, The centipede game, is an extensive form game in which two players take turns choosing either to take a little bit larger share of pot, or to pass the pot to the other player. The payoffs are arranged so that if one passes the pot to one's opponent and the other opponent takes the pot on the next round, one receives slightly less than if one had taken the pot on this round.

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