Dionysius Glycopantis

Differential Information Economies

Equilibrium concepts in differential information economies.- Core Notions, Existence Results.- Information, efficiency, and the core of an economy.- Information, efficiency and the core of an economy: Comments on Wilsons paper.- The core of an economy with differential information.- An alternative proof of the nonemptiness of the private core.- On the continuity of expected utility.- Market games with differential information and infinite dimensional commodity spaces: the core.- A two-stage core with applications to asset market and differential information economiesw.- Balancedness and the core in economies with asymmetric information.- Core and Walrasian Expectations Equilibrium Equivalence.- Competitive and core allocations in large economies with differential information.- Incentive compatible core and competitive equilibria in differential information economies.- Exchange economies with asymmetric information: competitive equilibrium and core.- Core, Pareto Optimality and Incentive Compatibility.- Incentive compatibility and information superiority of the core of an economy with differential information.- Efficiency and incentive compatibility in differential information economies.- Incentives in market games with asymmetric information: the core.- Cooperative interim contract and re-contract: Chandlers M-form firm.- Optimal multilateral contracts.- Risk aversion and incentive compatibility with ex post information asymmetry.- Ex ante contracting with endogenously determined communication plans.- Incentive compatible contractible information.- Continuity and Stability.- Core concepts in economies where information is almost complete.- On coalitional stability of anonymous interim mechanisms.- Signaling in markets with two-sided adverse selection.- Non-myopic learning in differential information economies: the core.- Value Allocations and the Bargaining SET.- Cooperative games with incomplete information.- The value allocation of an economy with differential information.- Existence and properties of a value allocation for an economy with differential information.- The bargaining set of a large economy with differential information.- Coalition structure values in differential information economies: Is unity a strength?.- Implementation.- Coalitional Bayesian Nash implementation in differential information economies.- An extensive form interpretation of the private core.- On extensive form implementation of contracts in differential information economies.

On extensive form implementation of contracts in differential information economies

In the context of differential information economies, with and without free disposal, we consider the concepts of Radner equilibrium, rational expectations equilibrium, private core, weak fine core and weak fine value. We look into the possible implementation of these concepts as perfect Bayesian or sequential equilibria of noncooperative dynamic formulations. We construct relevant game trees which indicate the sequence of decisions and the information sets, and explain the rules for calculating ex ante expected payoffs. The possibility of implementing an allocation is related to whether or not it is incentive compatible. Implementation through an exogenous third party or an endogenous intermediary is also considered.

An extensive form interpretation of the private core

The private core of an economy with differential information, (Yannelis (1991)), is the set of all state-wise feasible and private information measurable allocations which cannot be dominated, in terms of ex ante expected utility functions, by state-wise feasible and private information measurable net trades of any coalition. It is coalitionally Bayesian incentive compatible and also takes into account the information superiority of an individual. We provide a noncooperative extensive form interpretation of the private core for three person games. We construct game trees which indicate the sequence of decisions and the information sets, and explain the rules for calculating ex ante expected payoffs. In the spirit of the Nash programme, the private core is thus shown to be supported by the perfect Bayesian equilibrium of a noncooperative game. The discussion contributes not only to the development of ideas but also to the understanding of the dynamics of how coalitionally incentive compatible contracts can be realized.

The compactness of Pr (K)

We prove the compactness of Pr(K), the set of Borel probability measures on a compactum K endowed with the weak* topology, without embedding this set in rca(K), the space of regular, countably-additive, signed measures with their finite total variation as norm. Pr(K) can be extended to a convex, Hausdorff, linear topological space. Then Glicksberg’s fixed point theorem is applied to prove the existence of Nash equilibria.

On the solution of a stochastic optimal growth model

This note discusses a stochastic optimal growth model in which the optimal paths can be obtained by a simple direct argument. The structural characteristics of the model are the infinite horizon, the form of the instantaneous utility function, and uncertainty as a Wiener process in a linear production constraint. The note explains that, for optimality, at each point in time a formally identical problem must be solved. This implies that the optimal saving ratio must be constant.A proof, employing the rules of stochastic calculus, that the ensuing paths are the unique globally optimal paths is also given.

Nash Equilibria in Large Games

This paper adds to the discussion, in a general setting, that given a Nash-Schmeidler (nonanonymous) game it is not always possible to define a Mas-Colell (anonymous) game. In the two games, the players have different strategic behaviours and the formulations of the two problems are different. Also, we offer a novel explanation for the lack of a Nash equilibrium in an infinite game. We consider this game as the limit of a sequence of approximate, finite games for which an equilibrium exists. However, the limiting pure strategy function is not measurable.

A Tree Formulation for Signaling Games

We provide a detailed presentation and complete analysis of the sender/receiver Lewis signaling game using a game theory extensive form, decision tree formulation. The analysis employs well established game theory ideas and concepts. We establish the existence of four perfect Bayesian equilibria in this game. We explain which equilibrium is the most likely to prevail. Our explanation provides an essential step for understanding the formation of a language convention. Further, we discuss the informational content of such signals and calibrate a more detailed definition of a true (“correct”) signal in terms of the payoffs of the sender and the receiver.

Optimal decisions in two-stage bundling

We develop a generalised framework for pure bundling where buyer tastes for two goods are assumed to follow a normal distribution. In the literature optimal bundling decisions have been considered under the assumption that the weights of the two goods are Oxed and equal. The only consideration is then to choose the proOt maximising optimal price. Our approach is di§erent and much more realistic. The monopolist Orst decides on the optimal weights of the two goods and in the second stage derives the proOt maximising bundle price. Welfare and policy implications of our approach are derived and comparisons are made with those of the Oxed weights approach.

An Agency Relationship Under General Conditions of Uncertainty: The Case of the Doctor-Patient Interaction

The supply of information, particularly of bad news, in an agency relationship is a sensitive issue. We employ a game theory approach to investigate conflicts in the particular case of the doctor-patient relationship when information affects the emotions of patients. The doctor does not know the type of agent and the patient does not know how much information s/he is given. We show that the patient may non-adhere to the doctors recommendation not only when the doctor fails to identify the patients needs but also when the latter falsely believes that the doctor has not done so.

On Games with Imperfect Recall and Games with Perfect Recall

In the context of finite extensive form games, we consider games of imperfect and perfect recall. We look briefly at the famous Kuhn theorem. However we are mainly concerned with imperfect recall games in which paths can intersect information sets in more than one node. Explicit examples are given to examine a number of issues. We explain how optimal behaviour strategies are calculated. It is also argued that mixed behavioural strategies cannot always be captured by a behavioural strategy. We are considering the existence of a Nash equilibrium both in the case of mixed and of behavioural strategies. In order to make the discussion possible, starting with the players expected utilities in behavioural strategies in a polynomial form, a precise construction of a game tree is presented. In the case of existence of NE the solutions can imply identical or different pay-off vectors. A reference is also made to the recent discussion on the paradox of the absent-minded driver.