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Academic Commons Search Resultsen-usThe relation between implementability and the core
https://academiccommons.columbia.edu/catalog/ac:112686
Miyagawa, Eiichi10.7916/D8R502ZZMon, 12 Jun 2017 20:47:53 +0000This paper proves a simple and general theorem on resource-allocation mechanisms that achieve Pareto efficiency. We say that a mechanism (game form) is normal if at any action profile, an agent who obtains his endowments neither pays nor receives a positive amount. In the context of auctions, this simply means that losers receive no bill. We prove that for any normal mechanism, if its Nash equilibrium allocations are Pareto efficient for all preference profiles, then the equilibrium allocations are necessarily in the core. The result holds for a large class of allocation problems in which monetary transfers are feasible and the consumption space is discrete except for the space of transfers. Examples include auctions with any number of objects, economies with indivisible public goods, marriage problems, and coalition formation.Economicsem437EconomicsReportsReduced-form implementation
https://academiccommons.columbia.edu/catalog/ac:116566
Miyagawa, Eiichi10.7916/D8GM8KHCMon, 12 Jun 2017 20:47:52 +0000This paper studies resource-allocation mechanisms by using a reduced-form notion of mechanism. We formulate a mechanism by specifying the state space of the mechanism, the set of outcomes that agents can induce in a given state, and the set of admissible outcomes in each state. This notion of mechanism includes the Walrasian mechanism and majority voting as well as all game forms. With this notion, monotonicity is not only necessary but sufficient for a social choice correspondence to be implementable. Our main result is that in the context of exchange economies, if a mechanism implements a sub-correspondence of the Pareto correspondence and satisfies localness (one's "budget set" in a given state is independent of other agents' endowments), then the mechanism necessarily implements a sub-correspondence of the core correspondence. If the mechanism also satisfies anonymity, then it actually implements a sub-correspondence of the Walrasian equilibrium correspondence.Economicsem437EconomicsReportsRepeated games with observation costs
https://academiccommons.columbia.edu/catalog/ac:116428
Miyagawa, Eiichi; Miyahara, Yasuyuki; Sekiguchi, Tadashi10.7916/D8VX0TRWMon, 12 Jun 2017 20:47:48 +0000This paper analyzes repeated games in which it is possible for players to observe the other players' past actions without noise but it is costly. One's observation decision itself is not observable to the other players, and this private nature of monitoring activity makes it difficult to give the players proper incentives to monitor each other. We provide a sufficient condition for a feasible payoff vector to be approximated by a sequential equilibrium when the observation costs are sufficiently small. We then show that this result generates an approximate Folk Theorem for a wide class of repeated games with observation costs. The Folk Theorem holds for a variant of prisoners' dilemma, partnership games, and any games in which the players have an ability to "burn" small amounts of their own payoffs.Economicsem437EconomicsReportsThe folk theorem for repeated games with observation costs
https://academiccommons.columbia.edu/catalog/ac:115614
Miyagawa, Eiichi; Miyahara, Yasuyuki; Sekiguchi, Tadashi10.7916/D80P1B81Mon, 12 Jun 2017 20:47:47 +0000This paper studies repeated games with private monitoring where players make optimal decisions with respect to costly monitoring activities, just as they do with respect to stage-game actions. We consider the case where each player can observe other players' current-period actions accurately only if he incurs a certain level of disutility. In every period, players decide whether to monitor other players and whom to monitor. We show that the folk theorem holds for any finite stage game that satisfies the standard full dimensionality condition and for any level of observation costs. The theorem also holds under general structures of costless private signals and does not require explicit communication among the players. Therefore, tacit collusion can attain efficient outcomes in general repeated games with private monitoring if perfect private monitoring is merely feasible, however costly it may be.Economicsem437EconomicsReportsSubgame-perfect implementation of bargaining solutions
https://academiccommons.columbia.edu/catalog/ac:113924
Miyagawa, Eiichi10.7916/D8MC9B6NMon, 12 Jun 2017 20:47:44 +0000This paper provides simple four-stage game forms that fully implement a large class of two-person bargaining solutions in subgame-perfect equilibrium. The solutions that can be implemented by our game forms are those that maximize a monotonic and quasi-concave function of utilities after normalizing each agent's utility function so that the maximum utility is 1 and the utility of the disagreement outcome is 0. This class of solutions includes the Nash, Kalai, Smorodinsky, and Relative Utilitarian solutions. The game forms have a structure of alternating offers and contain no integer device.Economicsem437EconomicsReportsNonlinear pricing with self-control preferences
https://academiccommons.columbia.edu/catalog/ac:116126
Esteban, Susanna; Miyagawa, Eiichi; Shum, Matthew10.7916/D8000D91Mon, 12 Jun 2017 20:46:44 +0000This paper studies optimal nonlinear pricing for a monopolist when consumers' preferences exhibit temptation and self-control as in Gul and Pesendorfer (2001a). Consumers are subject to temptation inside the store but exercise self-control, and those foreseeing large self-control costs do not enter the store. Consumers differ in their preferences under temptation. When all consumers are tempted by more expensive, higher quality choices, the optimal menu is a singleton, which saves consumers from self-control and extracts consumers' commitment surplus. When some consumers are tempted by cheaper, lower quality choices, the optimal menu may contain a continuum of choices.Commerceem437EconomicsReportsRandom paths to stability in the roommate problem
https://academiccommons.columbia.edu/catalog/ac:112663
Diamantoudi, Effrosyni; Miyagawa, Eiichi; Xue, Licun10.7916/D8W66XZ5Mon, 12 Jun 2017 20:46:44 +0000This paper studies whether a sequence of myopic blockings leads to a stable matching in the roommate problem. We prove that if a stable matching exists and preferences are strict, then for any unstable matching, there exists a finite sequence of successive myopic blockings leading to a stable matching. This implies that, starting from any unstable matching, the process of allowing a randomly chosen blocking pair to form converges to a stable matching with probability one. This result generalizes those of Roth and Vande Vate (1990) and Chung (2000) under strict preferences.Economicsem437EconomicsReportsOptimal menu of menus with self-control preferences
https://academiccommons.columbia.edu/catalog/ac:115724
Esteban, Susanna; Miyagawa, Eiichi10.7916/D8V69WSBMon, 12 Jun 2017 20:46:43 +0000This paper studies how a seller should design its price schedule when consumers' preferences are subject to temptation. As in Gul and Pesendorfer (2001), consumers exercise costly self-control to some degree and foresee their impulsive behavior and self-control. Since consumers may pay a premium for an option set that is less tempting, the seller may offer multiple small menus. Building on the standard model of adverse selection and second-degree price discrimination, we characterize the optimal menu of menus for the seller. In particular, we show that if consumers are tempted by goods of higher quality, the seller can achieve perfect discrimination: consumers' choices appear as if the seller can observe consumers' preferences directly. To achieve this, the seller "decorates" menus by adding items that are never chosen but are tempting to consumers.Economicsem437EconomicsReports