Haruo Imai

The representative Nash solution for two-sided bargaining problems

Abstract An n -person bargaining situation is two-sided when participants of bargaining are divided into two groups and their preferences over bargained outcomes are exactly opposite to each other. This is so when the issue on the bargaining table is represented by a one dimensional set and people’s preferences are monotonically increasing in one group and monotonically decreasing in the other group. In this paper a solution for two-sided problems called the Representative Nash solution is introduced and axiomatized. A strategic bargaining model is constructed such that the unique stationary subgame perfect equilibrium outcome corresponds to the Representative Nash solution.

A characterization of a limit solution for finite horizon bargaining problems

We investigate a two-person random proposer bargaining game with a deadline. A bounded time interval is divided into bargaining periods of equal length and we study the limit of the subgame perfect equilibrium outcomes as the number of bargaining periods goes to infinity while the deadline is kept fixed. This limit is close to the discrete Raiffa solution when the time horizon is very short. If the deadline goes to infinity the limit outcome converges to the time preference Nash solution. Regarding this limit as a bargaining solution under deadline, we provide an axiomatic characterization.

Game Analysis of Kyoto and Post-Kyoto Schemes

Game theory is a tool utilized in economics to analyze the consequences of interaction among rational agents. It has been found to be especially useful for evaluating the workings of economic schemes at the theoretical level and also designing a possible mechanism to improve the economic system. In environmental economics, the use of game theory is most prominent in the analysis of IEAs (international environmental agreements), and the current negotiations on post-Kyoto (or post-2012) present a potential interesting application of game theory. Furthermore, such studies inspire further use of game theoretical tools in the study of such issues. In this chapter, we examine game theory analysis in this context and suggest some further directions of study with an emphasis on the role played by one particular mechanism under the Kyoto protocol (KP) called the CDM (clean development mechanism).

Pre-Negotiation for an International Emission Reduction Game

Based on a result due to Ray and Vohra showing the possibility of inefficiency due to a coalition formation in an international emission reduction game, we consider a possibility of negotiation preceding the negotiation stage, and by means of an example, indicate that the efficiency is restored. In the equilibrium obtained, we observe a potential in which different set of coalition arises in the two stages, which could help explain what is going on in the international negotiation.

Bilateral price-setting in a bilateral monopoly model

Abstract We consider a game model of a trade of one good between two firms, where both players first set prices and then choose quantities to be traded at the other players price. Investigating the outcome yielded by subgame perfect equilibria, we find that in a class of games called ‘regular cases’ subgame perfect equilibria in pure strategies always produce the ‘competitive outcome’. In general, subgame perfect equilibrium outcomes include other outcomes as well. In particular, when the cost curve or the revenue product curve is linear, the set of equilibrium outcomes contain the ‘monopolist outcome’ or the ‘monopsonist outcome’.

Emission Market at the End of the Commitment Period

We have several emission trading schemes at work currently and one eminent market among them is the one for GHG emissions under Kyoto Protocol starting 2009. For emissions to be tradable, property right must be securely set. Especially monitoring has to be reliable and timely, and leakage must be taken care of adequately. But this in turn implies that there is a discrepancy between the period where the amount of emission is ascertained and the period during which trading is supposedly bringing efficiency to the emission reduction. For instance, EU-ETS ended its first trading period at the end of 2007, but the emission level becomes available only after several months passed. Therefore, the so-called trueup period is necessary so that trading has to go on until the emission data are finalized. In the case of EU-ETS, the emission until 2007 can be traded till April 2008, and similar trueup period is set aside for the first commitment period of Kyoto Protocol.