A firm raises capital from multiple investors to fund a project. The project succeeds only if the... more A firm raises capital from multiple investors to fund a project. The project succeeds only if the capital raised exceeds a stochastic threshold, and the firm offers payments contingent on success. We study the firm’s optimal unique-implementation scheme, namely the scheme that guarantees the firm the maximum payoff. This scheme treats investors differently based on size. We show that if the distribution of the investment threshold is log-concave, larger investors receive higher net returns than smaller investors. Moreover, higher dispersion in investor size increases the firm’s payoff. Our analysis highlights strategic risk as an important potential driver of inequality. (JEL D21, D86, G24, G32)
We model situations in which a principal provides incentives to a group of agents to participate ... more We model situations in which a principal provides incentives to a group of agents to participate in a project (such as a social event or a commercial activity). Agents' benefits from participation depend on the identity of other participating agents. We assume bilateral exter- nalities and characterize the optimal incentive mechanism. Using a graph theoretic approach we show that the
We introduce emotions into an equilibrium notion. In a mental equilibrium each player "selec... more We introduce emotions into an equilibrium notion. In a mental equilibrium each player "selects" an emotional state which determines the player's preferences over the outcomes of the game. These preferences typically differ from the players' material preferences. The emotional states interact to play a Nash equilibrium and in addition each player's emotional state must be a best response (with respect to material preferences) to the emotional states of the others. We first discuss the concept behind the definition of mental equilibrium and show that this behavioral equilibrium notion organizes quite well the results of some of the most popular experiments in the literature of experimental economics. We expose some attractive properties of mental equilibria which are useful for deriving the set of mental equilibria for specific games.
We propose a model of gradual bargaining in the spirit of the Nash axiomatic theory. In this mode... more We propose a model of gradual bargaining in the spirit of the Nash axiomatic theory. In this model the underlying set of payoff opportunities expands continuously with time. Unlike Nash's solution that predicts a single agreement for each bargaining problem, our solution yields a continuous path of agreements--one for each point in time. It emerges from a simple and intuitive differential equation. We discuss the relationship between the gradual solution and various solution concepts of the standard Nash framework, and characterize it axiomatically with the essential axiom being "Invariance with Respect to Increasing Transformations". By using the richer framework of gradual bargaining, our axiomatization resolves a well known impossibility result by Shapley (1969), and it allows to construct an ordinal solution. Furthermore, our approach deals with some of the shortcomings of Nash's axiomatization. In particular, our axiomatic characterization does not use the con...
We propose two sequential mechanisms for ecient production of public goods. Our analysis diers fr... more We propose two sequential mechanisms for ecient production of public goods. Our analysis diers from the existing literature in al- lowing for the presence of multiple public goods and in also being "simple." While both mechanisms ensure eciency, the payos in the first mechanism are asymmetric, being sensitive to the order in which agents move. The second mechanism corrects for
We study a combinatorial variant of the classical principal-agent model. In our setting a princip... more We study a combinatorial variant of the classical principal-agent model. In our setting a principal wishes to incentivize a team of strategic agents to exert costly effort on his behalf. Agentsʼ actions are hidden and the principal observes only the outcome of the team, which depends stochastically on the complex combinations of the efforts by the agents. The principal seeks the mechanism that maximizes the principalʼs net revenue given an equilibrium behavior of the agents. We investigate the structure of the optimal mechanism for various production technologies as the principalʼs value from the project varies. In doing so we quantify the gap between the first-best and second-best solutions. Our results highlight the qualitative and quantitative differences between production technologies that exhibit complementarities and substitutabilities between the agentsʼ actions. In comparing the first best with the second best we highlight the role of effort monitoring by the principal. As we shall see, the benefit from monitoring crucially depends on the underlying technology, with the two polar cases being perfect substitution and perfect complementarity.
In this paper we analyze a principal's optimal monitoring strategies in a team environment. I... more In this paper we analyze a principal's optimal monitoring strategies in a team environment. In doing so we study the interaction between formal monitoring and informal (peer) monitoring. We show that if the technology satisfies complementarity, peer monitoring substitutes for the principal's monitoring. However, if the technology satisfies substitution, the principal's optimal monitoring is independent of the peer monitoring. We also show that if the technology satisfies complementarity, then the principal in the optimal contracts will monitor more closely than in the case of substitution. (JEL D23, D82, M54)
A firm raises capital from multiple investors to fund a project. The project succeeds only if the... more A firm raises capital from multiple investors to fund a project. The project succeeds only if the capital raised exceeds a stochastic threshold, and the firm offers payments contingent on success. We study the firm’s optimal unique-implementation scheme, namely the scheme that guarantees the firm the maximum payoff. This scheme treats investors differently based on size. We show that if the distribution of the investment threshold is log-concave, larger investors receive higher net returns than smaller investors. Moreover, higher dispersion in investor size increases the firm’s payoff. Our analysis highlights strategic risk as an important potential driver of inequality. (JEL D21, D86, G24, G32)
We model situations in which a principal provides incentives to a group of agents to participate ... more We model situations in which a principal provides incentives to a group of agents to participate in a project (such as a social event or a commercial activity). Agents' benefits from participation depend on the identity of other participating agents. We assume bilateral exter- nalities and characterize the optimal incentive mechanism. Using a graph theoretic approach we show that the
We introduce emotions into an equilibrium notion. In a mental equilibrium each player "selec... more We introduce emotions into an equilibrium notion. In a mental equilibrium each player "selects" an emotional state which determines the player's preferences over the outcomes of the game. These preferences typically differ from the players' material preferences. The emotional states interact to play a Nash equilibrium and in addition each player's emotional state must be a best response (with respect to material preferences) to the emotional states of the others. We first discuss the concept behind the definition of mental equilibrium and show that this behavioral equilibrium notion organizes quite well the results of some of the most popular experiments in the literature of experimental economics. We expose some attractive properties of mental equilibria which are useful for deriving the set of mental equilibria for specific games.
We propose a model of gradual bargaining in the spirit of the Nash axiomatic theory. In this mode... more We propose a model of gradual bargaining in the spirit of the Nash axiomatic theory. In this model the underlying set of payoff opportunities expands continuously with time. Unlike Nash's solution that predicts a single agreement for each bargaining problem, our solution yields a continuous path of agreements--one for each point in time. It emerges from a simple and intuitive differential equation. We discuss the relationship between the gradual solution and various solution concepts of the standard Nash framework, and characterize it axiomatically with the essential axiom being "Invariance with Respect to Increasing Transformations". By using the richer framework of gradual bargaining, our axiomatization resolves a well known impossibility result by Shapley (1969), and it allows to construct an ordinal solution. Furthermore, our approach deals with some of the shortcomings of Nash's axiomatization. In particular, our axiomatic characterization does not use the con...
We propose two sequential mechanisms for ecient production of public goods. Our analysis diers fr... more We propose two sequential mechanisms for ecient production of public goods. Our analysis diers from the existing literature in al- lowing for the presence of multiple public goods and in also being "simple." While both mechanisms ensure eciency, the payos in the first mechanism are asymmetric, being sensitive to the order in which agents move. The second mechanism corrects for
We study a combinatorial variant of the classical principal-agent model. In our setting a princip... more We study a combinatorial variant of the classical principal-agent model. In our setting a principal wishes to incentivize a team of strategic agents to exert costly effort on his behalf. Agentsʼ actions are hidden and the principal observes only the outcome of the team, which depends stochastically on the complex combinations of the efforts by the agents. The principal seeks the mechanism that maximizes the principalʼs net revenue given an equilibrium behavior of the agents. We investigate the structure of the optimal mechanism for various production technologies as the principalʼs value from the project varies. In doing so we quantify the gap between the first-best and second-best solutions. Our results highlight the qualitative and quantitative differences between production technologies that exhibit complementarities and substitutabilities between the agentsʼ actions. In comparing the first best with the second best we highlight the role of effort monitoring by the principal. As we shall see, the benefit from monitoring crucially depends on the underlying technology, with the two polar cases being perfect substitution and perfect complementarity.
In this paper we analyze a principal's optimal monitoring strategies in a team environment. I... more In this paper we analyze a principal's optimal monitoring strategies in a team environment. In doing so we study the interaction between formal monitoring and informal (peer) monitoring. We show that if the technology satisfies complementarity, peer monitoring substitutes for the principal's monitoring. However, if the technology satisfies substitution, the principal's optimal monitoring is independent of the peer monitoring. We also show that if the technology satisfies complementarity, then the principal in the optimal contracts will monitor more closely than in the case of substitution. (JEL D23, D82, M54)
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Papers by Eyal Winter