Implementation in adaptive better-response dynamics: Towards a general theory of bounded rationality in mechanisms.

We study the classic implementation problem under the behavioral assumption that agents myopically adjust their actions in the direction of better-responses or bestresponses. First, we show that a necessary condition for recurrent implementation in better-response dynamics (BRD) is a small variation of Maskin monotonicity, which we call quasimonotonicity. We also provide a mechanism for implementation in BRD if the rule is quasimonotonic and excludes worst alternatives – no worst alternative (NWA). Quasimonotonicity and NWA are both necessary and sufficient for absorbing implementation in BRD. Moreover, they characterize implementation in strict Nash equilibria. Under incomplete information, incentive compatibility is necessary for any kind of stable implementation in our sense, while Bayesian quasimonotonicity is necessary for recurrent implementation in interim BRD. Both conditions are also essentially sufficient for recurrent implementation, together with a Bayesian NWA. A characterization of implementation in strict Bayesian equilibria is also provided. Partial implementation results are also obtained.Robust implementation; Bounded rationality; Evolutionary dynamics; Mechanisms;

Stochastically stable implementation

Restricting attention to economic environments, we study implementation under perturbed better-response dynamics (BRD). A social choice function (SCF) is implementable in stochastically stable strategies of perturbed BRD whenever the only outcome supported by the stochastically stable strategies of the perturbed process is the outcome prescribed by the SCF. For uniform mistakes, we show that any ε-secure and strongly efficient SCF is implementable when there are at least five agents. Extensions to incomplete information environments are also obtained.Robust implementation, Bounded rationality, Evolutionary dynamics, Mechanisms, Stochastic stability

Stochastically stable implementation.

Restricting attention to economic environments, we study implementation under perturbed better-response dynamics (BRD). A social choice function (SCF) is implementable in stochastically stable strategies of perturbed BRD whenever the only outcome supported by the stochastically stable strategies of the perturbed process is the outcome prescribed by the SCF. For uniform mistakes, we show that any ε-secure and strongly efficient SCF is implementable when there are at least five agents. Extensions to incomplete information environments are also obtained.Robust implementation; Bounded rationality; Evolutionary dynamics; Mechanisms; Stochastic stability;

Implementation in adaptive better-response dynamics

We study the classic implementation problem under the behavioral assumption that agents myopically adjust their actions in the direction of better-responses within a given institution. We offer results both under complete and incomplete information. First, we show that a necessary condition for assymptotically stable implementation is a small variation of (Maskin) monotonicity, which we call quasimonotonicity. Under standard assumptions in economic environments, we also provide a mechanism for Nash implementation which has good dynamic properties if the rule is quasimonotonic. Thus, quasimonotonicity is both necessary and almost sufficient for assymptotically stable implementation. Under incomplete information, incentive compatibility is necessary for any kind of stable implementation in our sense, while Bayesian quasimonotonicity is necessary for assymptotically stable implementation. Both conditions are also essentially sufficient for assymptotically stable implementation. We then tighten the assumptions on preferences and mutation processes and provide mechanisms for stochastically stable implementation under more permissive conditions on social choice rules.implementation; bounded rationality; evolutionary dynamics; mechanisms

Implementation in Adaptive Better-Response Dynamics

We study the classic implementation problem under the behavioral assumption that agents myopically adjust their actions in the direction of better-responses within a given institution. We offer results both under complete and incomplete information. First, we show that a necessary condition for assymptotically stable implementation is a small variation of (Maskin) monotonicity, which we call quasimonotonicity. Under standard assumptions in economic environments, we also provide a mechanism for Nash implementation which has good dynamic properties if the rule is quasimonotonic. Thus, quasimonotonicity is both necessary and almost sufficient for assymptotically stable implementation. Under incomplete information, incentive compatibility is necessary for any kind of stable implementation in our sense, while Bayesian quasimonotonicity is necessary for assymptotically stable implementation. Both conditions are also essentially sufficient for assymptotically stable implementation. We then tighten the assumptions on preferences and mutation processes and provide mechanisms for stochastically stable implementation under more permissive conditions on social choice rules.

Entropy and the value of information for investors

Consider any investor who fears ruin facing any set of investments that satisfy noarbitrage. Before investing, he can purchase information about the state of nature in the form of an information structure. Given his prior, information structure α is more informative than information structure β if whenever he rejects α at some price, he also rejects β at that price. We show that this complete informativeness ordering is represented by the decrease in entropy of his beliefs, regardless of his preferences, initial wealth or investment problem. It is also shown that no prior-independent informativeness ordering based on similar premises exists.Informativeness, Information structures, Entropy, Decision under uncertainty, Investment, Blackwell ordering

Entropy and the value of information for investors

Consider any investor who fears ruin facing any set of investments that satisfy no-arbitrage. Before investing, he can purchase information about the state of nature in the form of an information structure. Given his prior, information structure alpha is more informative than information structure beta if whenever he rejects alpha at some price, he also rejects beta at that price. We show that this complete informativeness ordering is represented by the decrease in entropy of his beliefs, regardless of his preferences, initial wealth or investment problem. It is also shown that no prior-independent informativeness ordering based on similar premises exists.informativeness; information structures; entropy; decision under uncertainty; investment; Blackwell ordering

Implementation in adaptive better-response dynamics: Towards a general theory of bounded rationality in mechanisms

We study the classic implementation problem under the behavioral assumption that agents myopically adjust their actions in the direction of better-responses or bestresponses. First, we show that a necessary condition for recurrent implementation in better-response dynamics (BRD) is a small variation of Maskin monotonicity, which we call quasimonotonicity. We also provide a mechanism for implementation in BRD if the rule is quasimonotonic and excludes worst alternatives – no worst alternative (NWA). Quasimonotonicity and NWA are both necessary and sufficient for absorbing implementation in BRD. Moreover, they characterize implementation in strict Nash equilibria. Under incomplete information, incentive compatibility is necessary for any kind of stable implementation in our sense, while Bayesian quasimonotonicity is necessary for recurrent implementation in interim BRD. Both conditions are also essentially sufficient for recurrent implementation, together with a Bayesian NWA. A characterization of implementation in strict Bayesian equilibria is also provided. Partial implementation results are also obtained.Publicad