Game theory explains why you’re willing to pay more than a dollar for a dollar.
http://io9.com/5831215/how-game-theory-explains-why-youre-willing-to-sell-a-dollar-for-a-penny/
This article introduces the “dollar auction”. In this auction, two players are at an auction for a dollar. The only way to win the dollar is by bidding their own money. The twist to this auction is that both players must pay their auction amount upon “winning” the auction. Due to the nature of the costs to each player, when the bid reaches 99 cents, the only logical move for the other player is to bid a dollar such that they break even on the auction. After the dollar bid is placed; however, the other player who was once making 1 cent from the auction no longer wishes to loose his 99 cents, so he bids up another penny on the auction in order to minimize his “debt”. As can be seen, this process can continue indefinitely while both players are no longer benefiting themselves past the dollar bid.
This scenario is also referred to as a “war of attrition”. No dominant strategy exists for this game because if one player wins, the other player is worse off than when the game was started. Although there is no dominant strategy, a Nash Equilibrium for this game is possible. Equilibrium can only occur if one player bids zero and the other player bids a value equal to or greater than the dollar (the winning “value” of the auction, this can be generalized as a value V). Neither player can deviate from this strategy or else the equilibrium is not met. This way one player wins zero and pays zero while the other player minimizes their losses by bidding a value equal to V, and then must pay V which results in zero total value gained. This is commonly known as a “lose-lose” situation, where either contender will not make any gains from playing the game.
Examining the game even further and adding another twist that is common in reality introduces the idea of acting irrationally and bluffing. One can predict the outcomes of a war of attrition if all players act rationally, but if there is a possibility of one player deviation from a logical bid then strategy turns into one of “chicken” in which the players must “call” each other on bluffing.