Game theory, international law, and future environmental cooperation in the Middle East.

• Author: Hirsch, Moshe

1. INTRODUCTION

   Interdependence is an underlying factor within numerous transnational environmental systems. This interdependence generates an interactive decision-making setting in which a state's choice of action is contingent upon the expected behavior of other actors in the international arena. National decision-makers are aware that the quality and quantity of essential environmental resources available in their territories is determined not only by natural factors and their own behavior, but by the actions of other states.

   Attaining optimal results in an interactive situation frequently requires "collective action." Collective action occurs when the efforts of two or more individuals are needed to achieve a certain outcome, one which will typically further the interests or well-being of the group.(1) In terms of Pareto Optimality,(2) the course of action which leads to the best outcome for the group is cooperative behavior. The main problem with collective action occurs when a rational individual's behavior leads to Pareto inferior outcomes. This phenomenon often happens in large groups and in situations in which all individuals agree about the common good and the desirable means of achieving it.(3)

   In his seminal book, "The Logic of Collective Action", Mancur Olson rigorously presents the basic proposition that rational self-interested individuals frequently will not act in concert to achieve common interests.(4) The negative repercussions of Olson's proposition for international environmental cooperation increases together with the ratio of inter-state environmental independence. While environmental interdependence has long been apparent in the international arena, it has become increasingly prevalent in recent decades. In light of this rapidly growing trend, as well as the deterioration of essential environmental resources in most parts of the world, Olson's theory is particularly relevant to the international community today.

   The Middle East environmental system exemplifies both the need for and the impediments to successful regional collective action. Several diverse parties share the Middle East's primary environmental resources. Thus, when a party takes action in one jurisdiction it frequently affects environmental resources in neighboring areas.(5) Such interactive features characterize the Middle East's crucial water resources, marine environment and air basin. Some of the region's environmental resources are at significant risk and future developments may further imperil their sustainable utilization. The peace process, if successful, is expected to generate accelerated economic development and industrialization in the region, particularly in the West Bank and Gaza Strip. Increased economic development will place more pressure on the region's fragile resources.

   Efficient utilization of the Middle East's environmental resources requires the parties to establish and implement cooperative arrangements. In the past, armed conflicts in the Middle East precluded almost any environmental cooperation among the parties. Indeed, the first elaborated cooperative arrangements only emerged in 1994. The environmental provisions in the recently concluded agreements between Israel and its neighbors(6) have a clear bilateral character. However, optimal protection and utilization of the region's environmental resources frequently necessitates the establishment of cooperative arrangements on a regional level. Furthermore, the termination of hostilities does not ensure that an optimal framework for cooperation will emerge in the future. Recall Olson's proposition regarding collective action failure: rational self-interested actors frequently will not act to achieve their common interests, even when optimal results and the appropriate means of attaining them are agreed upon.

   Avoiding collective action failure in the Middle Eastern environmental system requires an examination of the factors motivating or hindering international cooperation.(7) Identification of these critical factors helps predict which environmental domains are more susceptible to collective action failure. Armed with an understanding of the impact of these factors, the challenge facing scholars of international law is to devise appropriate legal mechanisms to modify the structure of problematic settings to improve the prospects of cooperation.(8)

   Through the use of game theory, this article explores some of the principal factors influencing the emergence and maintenance of international cooperation in order to develop legal guidelines for establishing an effective environmental mechanism in the Middle East. As this article will show, game theory concepts and models provide a valuable tool for analyzing the phenomenon of cooperation, enabling international lawyers to shape legal norms which will enhance the prospects for environmental cooperation in the Middle East. Part II of this article sets forth the basic concepts and models of game theory and its relationship to modern international relations theory. Part III presents a game theoretical analysis of two major environmental settings in the Middle East: marine pollution in the Gulf of Aqaba and water contamination of the Mountain Aquifer. It then suggests some legal mechanisms to enhance the likelihood of cooperation in these settings. Part IV concludes the article by exploring the options and limits of combining game theory and international law as an instrument to improve the prospects of cooperation. The article ultimately states that this combination offers scholars and policy-makers important insights into better legal mechanisms for long-term international cooperation.

2. GAME THEORY AND COOPERATION

   1. Basic Elements of Game Theory(9)

      Mathematicians were the first to develop game theory, primarily for use in economics. Later, other disciplines, such as political science, international relations, law, sociology and biology also employed game theory concepts. Game theory is a strand of rational choice theory,(10) "designed to treat rigorously the question of [the] optimal behavior"(11) of decision-makers in "strategic" situations. The term "strategic" refers to situations in which the outcome does not depend solely on the decisionmaker's behavior or nature, but also on the behavior of other participants. An important factor shaping an individual's choice is the social setting or "structure" of a particular situation. Game theory enables social scientists to formalize social structures and then examine the implications of the structure on individual decisions.(12)

      A "game" is any interaction between players governed by a set of rules specifying the possible moves for each participant and a set of outcomes for each possible combination of moves. The decision-makers are assumed to be rational in the sense that they have certain goals, which they strive to attain through their actions. They have a consistent preference ordering of goals, know the rules of the game, and know that the other players are also rational.(13)

      Game theory represents interactions between participants in two principal forms: the normal (or strategic) form game and the extensive (or tree) form game. A matrix showing each player's payoff for each combination of strategies often represents a normal game. The normal representation is more appropriate for simultaneous decision-making while the extensive form is more suitable to sequential-move games. The latter form also displays the information each player knows when making his decisions.(14) The basic elements of the normal form game include: (1) the players--the actors who make the decisions (either individuals or collective decision-making units like firms or states); (2) the strategy space--the range of moves available to a player in a given situation (i.e., to cooperate or to defect); and (3) the payoffs (`utilities') - the outcome generated for the players from a chosen move or strategy.(15)

      A game theoretical analysis of social phenomena often does not allow for the allocation of accurate payoffs to expected outcomes. In some cases, it is possible to assign ordinal payoffs to expected outcomes (i.e., to organize the various outcomes in accordance with the order of priorities for the relevant player) and then to allocate a respective ordinal number to each outcome. This method leads to interesting inferences in numerous situations.(16) However, without knowing the "distance" between the payoffs on an interval scale, one cannot accurately calculate the probabilities with which each party would choose each outcome.(17)

      After reducing sets of interactions to a normal or extensive game, the next step is to determine the game's solution. Finding the "solution" of a game serves a normative goal, as it may reveal the best strategy for a rational player. It also serves a predictive aim, as it may indicate how rational players are likely to behave in such situations. A simple example is the notion of dominant strategy. A strategy is strictly dominant if it is a best strategy (i.e., it maximizes a player's payoff), regardless of the other player's actions. When it is possible to identify a single dominant strategy, one can safely assume that a rational player will adopt the dominant strategy. Conversely, by identifying dominated strategies, one can assume that rational players will not adopt them.(18)

      While a strict dominant strategy will not solve many games, the Nash-equilibrium solution applies to a much broader spectrum of cases. A Nash-equilibrium is the combination of strategies, representing the best response of each player to the predicted strategies of the other players. Such a prediction may be called "strategically stable" or "self-enforcing" because no single player is interested in deviating from the predicted strategy.(19)

      Game theory is divided into cooperative and non-cooperative game theory, based on the enforceability of agreements and...