12 research outputs found
Local Dominance
We define a local notion of dominance that speaks to the true choice problems
among actions in a game tree. When we do not restrict players' ability to do
contingent reasoning, a reduced strategy is weakly dominant if and only if it
prescribes a locally dominant action at every decision node, therefore any
dynamic decomposition of a direct mechanism that preserves strategy-proofness
is robust to the lack of global planning. Under a form of wishful thinking, we
also show that strategy-proofness is robust to the lack of forward planning.
Moreover, we identify simple forms of contingent reasoning and foresight,
driven by the local viewpoint. We construct a dynamic game that implements the
Top Trading Cycles allocation in locally dominant actions under these simple
forms of reasoning
Cautious Belief and Iterated Admissibility
We define notions of cautiousness and cautious belief to provide epistemic
conditions for iterated admissibility in finite games. We show that iterated
admissibility characterizes the behavioral implications of "cautious
rationality and common cautious belief in cautious rationality" in a terminal
lexicographic type structure. For arbitrary type structures, the behavioral
implications of these epistemic assumptions are characterized by the solution
concept of self-admissible set (Brandenburger, Friedenberg and Keisler 2008).
We also show that analogous conclusions hold under alternative epistemic
assumptions, in particular if cautiousness is "transparent" to the players.
KEYWORDS: Epistemic game theory, iterated admissibility, weak dominance,
lexicographic probability systems. JEL: C72
Backward induction reasoning beyond backward induction
Backward Induction is a fundamental concept in game theory. As an algorithm, it can only be used to analyze a very narrow class of games, but its logic is also invoked, albeit informally, in several solution concepts for games with imperfect or incomplete informa-tion (Subgame Perfect Equilibrium, Sequential Equilibrium, etc.). Yet, the very meaning of ‘backward induction reasoning’ is not clear in these settings, and we lack a way to apply this simple and compelling idea to more general games. We remedy this by introducing a solution concept for games with imperfect and incomplete information, Backwards Rational-izability, that captures precisely the implications of backward induction reasoning. We show that Backwards Rationalizability satisfies several properties that are normally ascribed to backward induction reasoning, such as: (i) an incomplete-information extension of subgame consistency (continuation-game consistency); (ii) the possibility, in finite horizon games, of being computed via a tractable backwards procedure; (iii) the view of unexpected moves as mistakes; (iv) a characterization of the robust predictions of a ‘perfect equilibrium’ notion that introduces the backward induction logic and nothing more into equilibrium analysis.
We also discuss a few applications, including a new version of peer-confirming equilibrium (Lipnowski and Sadler (2019)) that, thanks to the backward induction logic distilled by Backwards Rationalizability, restores in dynamic games the natural comparative statics the original concept only displays in static settings
Backward induction reasoning beyond backward induction
Backward Induction is a fundamental concept in game theory. As an algorithm, it can only be used to analyze a very narrow class of games, but its logic is also invoked, albeit informally, in several solution concepts for games with imperfect or incomplete informa-tion (Subgame Perfect Equilibrium, Sequential Equilibrium, etc.). Yet, the very meaning of ‘backward induction reasoning’ is not clear in these settings, and we lack a way to apply this simple and compelling idea to more general games. We remedy this by introducing a solution concept for games with imperfect and incomplete information, Backwards Rational-izability, that captures precisely the implications of backward induction reasoning. We show that Backwards Rationalizability satisfies several properties that are normally ascribed to backward induction reasoning, such as: (i) an incomplete-information extension of subgame consistency (continuation-game consistency); (ii) the possibility, in finite horizon games, of being computed via a tractable backwards procedure; (iii) the view of unexpected moves as mistakes; (iv) a characterization of the robust predictions of a ‘perfect equilibrium’ notion that introduces the backward induction logic and nothing more into equilibrium analysis.
We also discuss a few applications, including a new version of peer-confirming equilibrium (Lipnowski and Sadler (2019)) that, thanks to the backward induction logic distilled by Backwards Rationalizability, restores in dynamic games the natural comparative statics the original concept only displays in static settings
A case for transparency in principal-agent relationships
When is transparency optimal for the principal in principal-agent
relationships? We consider the following setting. The principal has private
information that affects the agent's incentives to exert effort. Higher effort
leads to higher material utility for both parties but the agent bears the cost
of effort. The principal can share her information with the agent and can
commit to any information structure. We obtain interpretable and easily
verifiable sufficient conditions for the optimality of full disclosure. With
this, we show that full disclosure is optimal under some modeling assumptions
commonly used in applied principal-agent papers
Belief change, rationality, and strategic reasoning in sequential games
A central aspect of strategic reasoning in sequential games consists in anticipating how co-players would react to information about past play, which in turn depends on how co-players update and revise their beliefs. Several notions of belief system have been used to model how players' beliefs change as they obtain new information, some imposing considerably more discipline than others on how beliefs at different information sets are related. We highlight the differences between these notions of belief system in terms of introspection about one's own conditional beliefs, but we also show that such differences do not affect the essential aspects of rational planning and the behavioral implications of strategic reasoning, as captured by rationalizability