such that b>V/2, they both lose b-V/2. Luce and Raiffa referred to the latter situation as a "ruinous situation"; both players suffer, and there is no winner. The conclusion one can draw from this pseudo-matrix is that there is no value to bid which is beneficial in all cases, so there is no dominant strategy. However, there are multiple asymmetric weak Nash Equilibria in pure strategies. For example, either player could commit to any bid b≥V. The other player's best response is to bid zero as there is no bid with which they can win the prize and receive a positive payoff. The player with the positive bid pays nothing in equilibrium. So, they have no incentive to bid less. This equilibrium is subgame perfect. There is also a symmetric equilibrium in mixed strategies. Symmetric Nash equilibrium Another popular formulation of the war of attrition is as follows: two players are involved in a dispute. The value of the object to each player is . Time is modeled as a continuous variable which starts at zero and runs indefinitely. Each player chooses when to concede the object to the other player. In the case of a tie, each player receives utility. Time is valuable, each player uses one unit of utility per period of time. This formulation is slightly more complex since it allows each player to assign a different value to the object. We assume that both players know the valuation of the other player. Thus, the game is a complete information game. The unique symmetric Nash equilibrium is defined by the following survival function for t: The value , for a player i whose opponent values the resource at over time t, is the probability that t ≥ x. This strategy does not guarantee the win for either player. Rather, it is the optimal strategy given that your opponent also plays a strategy of the same form. Note that if , So, the player with the lower value persists longer than the player with the higher value. This means that the player with the lower value has a higher probability of winning the war. Note that there does not exist any x such that the survival function equals zero. So, the distribution of bids has full support. Moreover, both players receive an expected payoff of zero because their payoff is zero at t=0 and their expected payoff must