Essays on equilibrium refinements

This dissertation contains two essays. The first essay considers an evolutionary game in which individuals have a payoff-irrelevant type and can take different actions conditional on their opponent type profile. The paper introduce a new assumption that a mutation in both the type and actions taken against opponents is an order of magnitude less likely than a mutation in only the type or actions. A pure strategy profile s is accessible from s' if there is one player who prefers s to s' and either this player's action is the same in both profiles or the two profiles differ only by this player's action. A set of strategy profiles is absorbing if it is a minimal closed set under accessibility. If all absorbing sets are singletons, all stochastically stable outcomes are strict Nash equilibria. At the same time, all Pareto undominated absorbing sets are stochastically stable, whether they are risk-dominant or not. In a common interests game, the only stochastically stable payoff vector is the efficient payoff vector. These results apply to generic games in general while also having special implications on coordination games and games in which interests along accessible paths are aligned.;The second essay proposes a refinement of Nash equilibria by selecting those consistent with the decision theoretic axiom of forward induction. Forward induction is the notion that individuals rationalize their opponents' behaviors even when confronted with an unexpected event. An admissible, invariant forward induction equilibrium concept is constructed. Forward induction equilibrium exists for all finite generic extensive form games with perfect recall. It does not satisfy backward induction. Yet for generic extensive form games the set of forward induction outcomes contains an invariant backward induction equilibrium outcome. Forward induction is not equivalent to iterative elimination of dominated strategies. It encompasses most commonly used refinements for signaling games.