Invariance under type morphisms: the bayesian Nash equilibrium

Ely and Peski (2006) and Friedenberg and Meier (2010) provide examples when changing the type space behind a game, taking a "bigger" type space, induces changes of Bayesian Nash Equilibria, in other words, the Bayesian Nash Equilibrium is not invariant under type morphisms. In this paper we introduce the notion of strong type morphism. Strong type morphisms are stronger than ordinary and conditional type morphisms (Ely and Peski, 2006), and we show that Bayesian Nash Equilibria are not invariant under strong type morphisms either. We present our results in a very simple, finite setting, and conclude that there is no chance to get reasonable assumptions for Bayesian Nash Equilibria to be invariant under any kind of reasonable type morphisms.

Transferable Utility Games with Uncertainty

We introduce the concept of a TUU-game, a transferable utility game with uncertainty. In a TUU-game there is uncertainty regarding the payoffs of coalitions. One out of a finite number of states of nature materializes and conditional on the state, the players are involved in a particular transferable utility game. We consider the case without ex ante commitment possibilities and propose the Weak Sequential Core as a solution concept. We characterize the Weak Sequential Core and show that it is non-empty if all ex post TUgames are convex.

Transferable Utility Games with Uncertainty

We introduce the concept of a TUU-game, a transferableutilitygame with uncertainty. In a TUU-game there is uncertainty regarding the payoffs of coalitions. One out of a finite number of states of nature materializes and conditional on the state, the players are involved in a particular transferableutilitygame. We consider the case without ex ante commitment possibilities and propose the Weak Sequential Core as a solution concept. We characterize the Weak Sequential Core and show that it is non-empty if all ex post TU-games are convex.

State subsidy and moral hazard in corporate financing

This paper investigates the impact of state subsidy on the behavior of the entrepreneur under asymmetric information. Several authors formulated concerns about state intervention as it can aggravate moral hazard in corporate financing. In the seminal paper of Holmström and Tirole (1997) a two-player moral hazard model is presented with an entrepreneur initiating a risky scalable project and a private investor (e.g. bank or venture capitalist) providing outside financing. The novelty of our research is that this basic moral hazard model is extended to the case of positive externalities and to three players by introducing the state subsidizing the project. It is shown that in the optimum, state subsidy does not harm, but improves the incentives of the entrepreneur to make efforts for the success of the project; hence in effect state intervention reduces moral hazard. Consequently, state subsidy increases social welfare which is defined as the sum of private and public net benefits. Also, the exact form of the state subsidy (ex-ante/ex-post, conditional/unconditional, refundable/nonrefundable) is irrelevant in respect of the optimal size and the total welfare effect of the project. Moreover, in case of nonrefundable subsidies state does not crowd out private investors; but on the contrary, by providing additional capital it boosts private financing. In case of refundable subsidies some crowding effects may occur depending on the subsidy form and the parameters.