Pearce (1984) shows that in finite games, iterative elimination of weakly dominated strategies converges to the same set as admissibility, suggesting the two criteria are extensionally equivalent in relevant cases.

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Reasons For

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Reason for

1.Finite games have complete strategy spaces, making iterative elimination processes deterministic and comparable to axiomatic criteria like admissibility.
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2.Pearce's convergence result provides empirical evidence that two independently motivated solution concepts yield identical predictions in relevant domains.
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3.Extensional equivalence in finite games justifies treating admissibility and iterated weak dominance elimination as interchangeable for practical analysis.
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Reasons Against

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Reason against

1.Convergence to the same set does not establish conceptual equivalence; different logical paths to identical outcomes can reflect fundamentally different normative commitments.
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2.Pearce's result may depend on restrictive conditions (e.g., specific game structures) that limit generalizability beyond the cases where equivalence was demonstrated.
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3.Extensional equivalence in finite games tells us nothing about infinite games or continuous strategy spaces where the two criteria may diverge significantly.
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Key Terms

Finite games(describing the type of game situation being analyzed): Games where there are a limited number of players, a limited number of possible moves, and the game eventually ends (as opposed to games that could go on forever).
Iterative elimination of weakly dominated strategies(one method for solving or simplifying strategic games): A step-by-step process where you repeatedly remove choices that are never the best option for a player, even considering what other players might do; you keep removing these bad choices until no more can be removed.
Pearce (1984)(identifying the source of a mathematical proof about games): David Pearce is a game theorist who published influential work in 1984 about how to solve strategic decision problems; this citation refers to that specific publication.
Weakly dominated strategies(describing types of moves that rational players should avoid): A choice or plan of action in a game that is never better than some other choice, and sometimes worse, no matter what your opponent does.
admissibility(Game-theoretic decision theory; contrasted with the weaker condition of not being strictly dominated): A strategy is admissible if it is a best response to a belief (probability measure) that assigns positive probability to every possible choice of the opponents — i.e., a full-support probability measure
extensionally equivalent(Applied to Church's thesis and Turing's thesis regarding functions of positive integers): Two theses are extensionally equivalent when they are about one and the same class of functions

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A strategy that is not strictly dominated need not be admissible Convergence to the same set does not establish conceptual equivalence; different...

Details

Type: claim
Perspectives: 2 (1 for, 1 against)
Edits: 1 edit