POLI 388                                                                                                                        Spring 2005

The Dollar Auction Game

            “The Bank” tells P1 and P2 that one of them will win a prize of $100. Each of P1 and P2 will alternately pay $1 or more to the Bank until one player decides to stop paying and to pull out of the competition (i.e., to “give in”), at which point the other player (who has “stood firm”) wins the $100 prize. This can be thought of as auctioning off the prize to the highest bidder (hence the name of the game), with the twist that both bidders must pay their final offers, though only the player who made the higher final offer gets the prize. How will this game end up? (The Bank makes sure that P1 and P2 cannot enter into an enforceable agreement before the bidding starts.)

The Iterated Enduring Conflict Game (Endurance Contest or Contest of Wills)

            P1 and P2 are in contest (e.g., military fight) to win control a stake/prize (e.g., territory) worth 100 units of payoff. At each iteration of the game, each player must decide whether to “keep on fighting” in hope of winning the stake by outlasting the other player of whether to “give in” (or “pull out”) and concede the stake to the other player. The cost of fighting for another next iteration is 1 unit of payoff. The k be the number of iterations the game has already gone on. Thus the payoff matrix for the next iteration is the following.

            When (if ever) should a player pull out? Note that fight on “almost dominates” pull out because the cost of fighting previous iterations is a “sunk cost” that you cannot recoup whatever you do. Thus such an enduring conflict is an “almost Prisoner’s Dilemma.”