 The existence of self-ratifying mixed strategies in decision problems such as Death in Damascus suggests that ratification, as causal decision theory explains it, supports participation in a Nash equilibrium of a game. Such an equilibrium assigns a strategy to each player so that each strategy in the assignment is a best response to the others. Suppose that two people are playing Matching Pennies. Simultaneously, each displays a penny. One player tries to make the sides match, and the other player tries to prevent a match. If the first player succeeds, he gets both pennies. Otherwise, the second player gets both pennies. Suppose that each player is good at predicting the other player, and each player knows this. Then if the first player displays heads, he has reason to think that the second player displays tails. Also, if the first player displays tails, he has reason to think that the second player displays heads. Because Matching Pennies is a simultaneous-move game, neither player’s strategy influences the other player’s strategy, but each player’s strategy is evidence of the other player’s strategy. Mixed strategies help resolve decision instability in this case. If the first player flips his penny to settle the side to display, then his mixed strategy is self-ratifying. The second player’s situation is similar, and she also reaches a self-ratifying strategy by flipping her penny. The combination of self-ratifying strategies is a Nash equilibrium of the game.