Implementation of Subgame-Perfect Cooperative Agreement in an Extensive-Form Game

A novel approach to sustainable cooperation called subgameperfect core (S-P Core) was introduced by P. Chander and M. Wooders in 2020 for n-person extensive-form games with terminal payoffs. This solution concept incorporates both subgame perfection and cooperation incentives and implies certain distribution of the total players' payoff at the terminal node of the cooperative history. We use in the paper an extension of the S-P Core to the class of extensive games with payoffs defined at all nodes of the game tree that is based on designing an appropriate payoff distribution procedure β and its implementation when a game unfolds along the cooperative history. The difference is that in accordance with this so-called β-subgameperfect core the players can redistribute total current payoff at each node in the cooperative path. Moreover, a payoff distribution procedure from the β-S-P Core satisfies a number of good properties such as subgame efficiency, non-negativity and strict balance condition. In the paper, we examine different properties of the β-S-P Core, introduce several refinements of this cooperative solution and provide examples of its implementation in extensive-form games. Finally, we consider an application of the β-S-P Core to the symmetric discrete-time alternating-move model of fishery management.

Revealed Preference Implications of Backward Induction and Subgame Perfection

Consider a decision-maker (DM) who must select an alternative from a set of mutually exclusive alternatives but must take this decision sequentially. If the DM’s choice correspondence over subsets of alternatives satisfies the weak axiom of revealed preference (WARP), then the subgame perfect Nash equilibrium (SPNE) and backward induction (BI) strategies coincide. We study the relation between the SPNE and BI strategies when the DM’s choice correspondence fails to satisfy WARP. First, Sen’s axiom α is necessary and sufficient for the set of SPNE strategies to be a subset of the set of BI strategies; moreover, a mild strengthening of Sen’s axiom β is necessary and sufficient for the set of BI strategies to be a subset of the set of SPNE strategies. These results extend to multiplayer games. (JEL D11, C72, C73)

The Law Enforcement Of The Employees Social Security System In Indonesia: A Game Theory Perspective

Insurance for the workers means a guarantee of safety for their works on the workplaces. It is necessarily crucial as workers need such a policy that can protect them from the loss. Indonesian government declare a policy that enact the act about National Social Security System (SJSN). The companies are the subject of this regulation, despite the fact at the initial implementation of this law enforcement brought to the pros and cons. Hence, the regulation also regulates for those who betray the policy will have to pay some certain amount of fine which in turn can harden them. The companies on the other side have a choice either to register or not their workers to SJSN as they still consider the premium they have to pay. This study aims to analyze the payoffs for both government and companies to be better off from the law enforcement. Game theory perspective is applied for the methodology of the study, particularly Subgame Perfection Nash Equilibrium (SPNE) and Bayesian Nash Equilibrium (BNE). The results present that in condition of an effective law enforcement at p, the firms will be beneficial from the SJSN policy by registering their workers and pay the premium, because if they do not pay the premium they have to pay additional amount of fine. On the other hand, if the policy is not effective with 1-p, the firms will have an advantage by not registering their employees to the SJSN as the law enforcement is not effective. Also, the government does not necessarily conduct an investigation as the cost is higher than the return that they will get.

The Inefficiency of Nash and Subgame Perfect Equilibria for Network Routing

This paper provides new bounds on the quality of equilibria in finite congestion games with affine cost functions, specifically for atomic network routing games. It is well known that the price of anarchy equals exactly 5/2 in general. For symmetric network routing games, it is at most (5n − 2)/(2n + 1), where n is the number of players. This paper answers to two open questions for congestion games. First, we show that the price of anarchy bound (5n − 2)/(2n + 1) is tight for symmetric network routing games, thereby answering a decade-old open question. Second, we ask whether sequential play and subgame perfection allows to evade worst-case Nash equilibria, and thereby reduces the price of anarchy. This is motivated by positive results for congestion games with a small number of players, as well as recent results for other resource allocation problems. Our main result is the perhaps surprising proof that subgame perfect equilibria of sequential symmetric network routing games with linear cost functions can have an unbounded price of anarchy. We complete the picture by analyzing the case with two players: we show that the sequential price of anarchy equals 7/5 and that computing the outcome of a subgame perfect equilibrium is NP-hard.

Ideal Reactive Equilibrium

Refinements of the Nash equilibrium have followed the strategy of extending the idea of subgame perfection to incomplete information games. This has been achieved by appropriately restricting beliefs at unreached information sets. Each new refinement gives stricter and more mathematically-complicated limitations on permitted beliefs. A simpler approach is taken here, where the whole idea of beliefs is dispensed with, and a new equilibrium concept, called the ideal reactive equilibrium, that builds on some pioneering work by Amershi, Sadanand and Sadanand on thought process dynamics, is developed.

Game Theory and Security Studies

This chapter describes the basic assumptions of game theory and illustrates its major concepts, using examples drawn from the security studies literature. An arms race game is used as an example of a strategic form game, illustrating the meaning of an equilibrium outcome and the definition of a dominant strategy. Backward induction and the definition of subgame perfection are explained in the context of an extensive form game that features threats. Nash equilibrium and the Bayesian equilibrium are discussed, and a short review of the many applications of game theory in international politics is provided. Finally, the chapter concludes with a discussion of the usefulness of game theory in generating insights about deterrence.