Abstract:

This paper aims to provide a representation theorem for consumption stream in the simplex in continuous time, by using the weaker axiom of ”Agree with”, the strong axiom of “Preferential Independence”, and the axioms of “Separability” and “Measurability” on the simplex, consistent with the spirit of Koopman’s work between 1960-1972, and Epstein’s work in 1983 and 2003. Moreover, it considers a model containing piecewise continuous trajectories on the simplex, such as a portfolio optimization problem, a cake-cutting problem, or a maximization problem with a fixed budget (i,e., time, asset, probability distributions, etc.), which also allows some discontinuous trajectories. 

Abstract:

Dominance solvability is one of the simplest and most robust solution concepts first introduced by Moulin (1979)[8] in the context of voting. In contrast, it is rare to come across a game that does not have a strongly (or weakly) dominated strategy for which it would be difficult to characterize. Due to the high time complexity of this question, it is difficult to determine if one agent does not have a strictly dominated strategy. Hence, this study provides two major contributions: computational and economic. First, we show that the probability will go to 1 if M equals N and increases to infinity, moreover there exists a threshold of M while M does not necessarily equal N. In addition, we show this threshold is tight. A second advantage of this work is that it provides an efficient algorithm instead of the natural one discussed above, which reduces the time complexity to O(M (M − 1)N ) from O(M (M − 1 + λlog(N )), where λ is the constant.

Abstract:

Theoretically, this work relaxes the rationality behind IESDS in the normal-form game and Backward Induction in the extensive-form game, namely common p-believe in rationality in the normal-form game and common p-belief in the opponent’s future rationality in the extensive-form game. Exper- imentally, this work uses the experimental data from Masaki, Guillaume, and Sevgi (2023)[1] to verify the result.