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Sequential equilibrium
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<h2 id="consistent-assessments">Consistent assessments</h2> <p>The formal definition of a strategy being sensible given a belief is straightforward; the strategy should simply maximize expected payoff in every information set. It is also straightforward to define what a sensible belief should be for those information sets that are reached with positive probability given the strategies; the beliefs should be the conditional probability distribution on the nodes of the information set, given that it is reached. This entails the application of Bayes' rule. </p><p>It is far from straightforward to define what a sensible belief should be for those information sets that are reached with probability zero, given the strategies. Indeed, this is the main conceptual contribution of Kreps and Wilson. Their consistency requirement is the following: The assessment should be a <a href="/facts/Limit_point/95MykoGU">limit point</a> of a sequence of <a href="/facts/Mixed_strategy/VEXD1jyj">totally mixed</a> strategy profiles and associated sensible beliefs, in the above straightforward sense. </p> <h2 id="relationship-to-other-equilibrium-refinements">Relationship to other equilibrium refinements</h2> <p>Sequential equilibrium is a further refinement of <a href="/facts/Subgame_perfect_equilibrium/cyyhua3F">subgame perfect equilibrium</a> and even <a href="/facts/Bayesian_game/pHqJ1Tsn">perfect Bayesian equilibrium</a>. It is itself refined by extensive-form <a href="/facts/Trembling_hand_perfect_equilibrium/cm9Ftms4">trembling hand perfect equilibrium</a> and <a href="/facts/Proper_equilibrium/TVJpvjph">proper equilibrium</a>. Strategies of sequential equilibria (or even extensive-form <a href="/facts/Trembling_hand_perfect_equilibrium/cm9Ftms4">trembling hand perfect equilibria</a>) are not necessarily <a href="/facts/Admissible_decision_rule/Kmw4R8Gz">admissible</a>. A refinement of sequential equilibrium that guarantees admissibility is <a href="/facts/Quasi-perfect_equilibrium/NW7FQvAU">quasi-perfect equilibrium</a>. </p> <p><a href="/facts/David_M._Kreps/xAIRlHVk">David M. Kreps</a> and <a href="/facts/Robert_B._Wilson/SdPtXzWV">Robert Wilson</a>. "Sequential Equilibria", <i>Econometrica</i> 50:863-894, 1982. </p><p><a href="/facts/Roger_B._Myerson/wqJUCULP">Roger B. Myerson</a>. <i>Game Theory: Analysis of Conflict</i>, 1991. </p>