Constructive proof of the existence of Nash Equilibrium in a finite strategic game with sequentially locally non-constant payoff functions by Sperner's lemma

Using Sperner's lemma for modified partition of a simplex we will constructively prove the existence of a Nash equilibrium in a finite strategic game with sequentially locally non-constant payoff functions. We follow the Bishop style constructive mathematics

Strategy-proofness of social choice functions and non-negative association property with continuous preferences

We consider the relation between strategy-proofness of resolute (single-valued) social choice functions and its property which we call Non-negative association property (NNAP) when individual preferences over infinite number of alternatives are continuous, and the set of alternatives is a metric space. NNAP is a weaker version of Strong positive association property (SPAP) of Muller and Satterthwaite(1977). Barbera and Peleg(1990) showed that strategy-proofness of resolute social choice functions implies Modified strong positive association property (MSPAP). But MSPAP is not equivalent to strategy-proofness. We shall show that strategy-proofness and NNAP are equivalent for resolute social choice functions with continuous preferences.continuous preferences

Generalized monotonicity and strategy-proofness: A note

In this note we define generalized monotonicity which is a generalized version of monotonicity due to Muller and Satterthwaite (1979) for a social choice function under individual preferences which permit indifference, and shall show that generalized monotonicity and strategy-proofness are equivalent.generalized monotonicity

A topological proof of Eliaz's unified theorem of social choice theory (forthcoming in "Applied Mathematics and Computation")

Recently Eliaz(2004) has presented a unified framework to study (Arrovian) social welfare functions and non-binary social choice functions based on the concept of 'preference reversal'. He showed that social choice rules which satisfy the property of preference reversal and a variant of the Pareto principle are dictatorial. This result includes the Arrow impossibility theorem and the Gibbard-Satterthwaite theorem as its special cases. We present a concise proof of his theorem using elementary concepts of algebraic topology such as homomorphisms of homology groups of simplicial complexes induced by simplicial mappings.

Generalized monotonicity and strategy-proofness for non-resolute social choice correspondences

Recently there are several works which analyzed the strategy-proofness of non-resolute social choice rules such as Duggan and Schwartz (2000) and Ching and Zhou (2001). In these analyses it was assumed that individual preferences are linear, that is, they excluded indifference from individual preferences. We present an analysis of the strategy-proofness of non-resolute social choice rules when indifference in individual preferences is allowed. Following to the definition of the strategy-proofness by Ching and Zhou (2001) we shall show that a generalized version of monotonicity and the strategy-proofness are equivalent. It is an extension of the equivalence of monotonicity and the strategy-proofness for resolute social choice rules with linear individual preferences proved by Muller and Satterthwate (1980) to the case of non-resolute social choice rules with general individual preferences.generalized monotonicity