Iterated elimination of strictly dominated strategies is an order dependent procedure. It can also generate spurious Nash equilibria, fail to converge in countable steps, or converge to empty strategy sets. If best replies are well–defined, then spurious Nash equilibria cannot appear; if strategy spaces are compact and payoff functions are uppersemicontinuous in own strategies, then order does not matter; if strategy sets are compact and payoff functions are continuous in all strategies, then a unique and nonempty maximal reduction exists. These positive results extend neither to the better–reply secure games for which Reny has established the existence of a Nash equilibrium, nor to games in which (under iterated eliminations) any dominated strategy has an undominated dominator.

We examine experimentally the impact of communication on trust and cooperation. Our design admits observation of promises, lies, and beliefs. The evidence is consistent with people striving to live up to others' expectations so as to avoid guilt, as can be modeled using psychological game theory. When players exhibit such guilt aversion, communication may influence motivation and behavior by influencing beliefs about beliefs. Promises may enhance trustworthy behavior, which is what we observe. We argue that guilt aversion may be relevant for understanding strategic interaction in a variety of settings, and that it may shed light on the role of language, discussions, agreements, and social norms in these contexts.