Game Theory, International Law, and Future Environmental Cooperation in the Middle East

Beginning of article

I. 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.

II. GAME THEORY AND COOPERATION

A. 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 communication. Cooperative game theory assumes the existence of an institution capable of enforcing the agreements concluded between the players; whereas non-cooperative game theory assumes no such institution exists. In cooperative games, communication between the players is allowed while in non-cooperative games, communication may or may not be allowed.(20) Due to the lack of a central enforcement mechanism within the current international system, this study is concerned with non-cooperative games.

B. Game Theory and Modern International Relations Theory

The basic assumptions of game theory are compatible with the basic assumptions of modern international relations theory. Prevailing international relations theory assumes that: (1) States are the central actors in the international system; (2) States are not subordinated to a central international authority to enforce cooperation; (3) States are egoists - they constantly try to maximize their interests; and (4) States are rational - they have consistent, ordered preferences, which derive from calculating the costs and benefits of alternative courses of action.(21) Clearly, assumptions (2), (3) and (4) are consistent with those of non-cooperative game theory. Meanwhile, assumption (1) in no way contradicts any of the underlying premises of game theory.(22)

The concepts fundamental to international regimes, game theory and cooperation, are interrelated.(23) Game theory explains the conditions under which international regimes arise as an instance of cooperation, suggesting conditions conducive to stable compliance with them. Generally, international cooperation is a prerequisite to the establishment of international regimes.(24) However, cooperation, particularly short-term cooperation, can take place without the existence of international regimes.(25) Nonetheless in most cases, the creation of international regimes facilitates the establishment of long-term cooperative patterns between States.

While game theory provides a valuable tool for analysis of international cooperation, game theoretical models do not take into account various factors which frequently affect international cooperation. Such missing factors include the personal characteristics of decision-makers, as well as the social and moral values prevailing in their respective environments. On the other hand, game theoretical models do not attempt to address all factors relevant to collective action. Rather, they aim to simplify and abstract reality by focusing on certain factors of collective action while exploring the interplay among them. Such an analysis seems simplistic, but the simplification proves useful in clarifying complex interactions.(26)

Despite the imperfections which come from focusing on one set of variables, and the difficulties associated with assigning numerical payoffs to expected outcomes, game theoretical analysis sets forth the expected trends of decision-makers as well as the decisions likely to be adopted in particular settings. Furthermore, game theoretical analysis frequently provides scholars and policy-makers with insights regarding mechanisms designed to elicit and support stable cooperation.

C. Models of Collective Action

Each of the many collective action models presents a different payoff structure. This section presents the widely discussed models in game theoretical and international relations literature. After clarifying the basic features of each model, this section focuses on the prospects for cooperation in each setting. It should be noted that the Middle Eastern environmental settings do not accurately reflect the game theoretical models presented here. Frequently, however, it is possible to identify a particular environmental setting which presents strong features of a certain game theoretical model. As such, the insights drawn from the models presented below provide important indications regarding the expected trends of the decision-makers in these environmental settings.

1. Zero-Sum Games

Zero-sum game is one of game theory's most famous models. Particularly during the early stages of the theory's development, zero-sum game served as a polar case and historical point of departure. The key feature of zero-sum game is that the sum generated for the players for each possible combination of moves is zero. A game in which the sum of the payoffs is always constant (not necessarily zero) is called "constant-sum game" and its strategic analysis is equivalent to zero-sum game. In zero-sum games, whatever one player wins the other loses.(27) Since the payoffs to Player 2 are equal to the negative payoffs to Player 1, it is possible to simplify the strategic form and only write the payoffs of Player 1. Figure 1 illustrates the payoff matrix for a two-person zero-sum game:(28)

             Player 2

                  S1   S2

Player 1    S1    2     2
            S2    1     3

Figure 1: A Two-Player Zero-Sum Game

The solution to a zero-sum game, as suggested by Von Neumann and Morgenstern, involves the Maximin Principle, which directs players to maximize their security levels. The security level is the least amount that a player can receive from his move. The result of this game is an equilibrium pair in cell S1S1 generating 2 payoffs to Player 1, and -2 to Player 2.(29) This cell is called the "saddle-point." However, not all zero-sum games have a saddle-point.(30) The Maximin Principle is not only valid for a one-shot game, but applies to iterated games as well.(31)

Two-player zero-sum games represent strictly competitive situations. The players maintain opposing preferences and are considered rivals. As such, the players are in conflict and not inclined to cooperate.(32) Zero-sum games may have more than two players (N-players games) and some players may have an interest in cooperating against the rest of the players (i.e., in forming a coalition).(33) As one might imagine, a two player zero-sum game represents one of the worst models for international cooperation.

Similar levels of competitiveness also exist in non-zero-sum. These are games in which the players seek relative rather than absolute gains (i.e., in military contexts where the aim is to achieve superiority). When the game has only two players who are exclusively interested in relative gains, the situation can be modeled as a zero-sum game with no room for cooperation. The conflict diminishes significantly when there are more than two players, or if the concern for relative gains is less than total.(34)

Pure zero-sum situations rarely arise in the international arena, if at all. Strong features of zero-sum games are present in some international settings such as wars or sovereignty disputes over a particular territory.(35) Fortunately, the utilization of common environmental resources almost never represents a zero-sum game. Most international environmental resources are renewable. Thus, the sum of quantities available to the parties is not constant, rather it depends significantly upon the players' strategies. However, use of a shared, non-renewable environmental resource, like fossil water reservoirs,(36) may lead the parties to adopt strategies commonly employed in zero-sum games.

2. The Prisoner's Dilemma

The models discussed in the remainder of this section represent non-zero-sum games, the most famous of which is the Prisoner's Dilemma ("PD").(37) The PD model attracted considerable attention from both game theorists and scientists in various disciplines because the game's implications apply to a wide range of social phenomena. The normal form of PD is presented in Figure 2: let C (Cooperate) equal "not confess;" and D (Defect) equal "confess." By convention, the first payoff in each cell is to the row player, and the second payoff is to the column player.

                    Player 2

                     C         D

Player 1    C    0.5, 0.5    5, 0
            D    0,5         2,2

Figure 2: Prisoner's Dilemma

From Player 1's perspective; if Player 2 chooses strategy C or D, then Player 1 prefers D to C. Thus, strategy D strictly dominates strategy C. The same analysis holds true for Player 2, as C is strictly dominated by D. The result is that D is the dominant strategy for both players and cell DD represents the only Nash equilibrium for PD. As explained above, in Nash equilibrium, no player is interested in deviating from his predicted strategy.(38) The result generated in DD (2,2) is sub-optimal for both players who strongly prefer the result of CC (0.5, 0.5). PD represents a collective action failure. Since each rational player is not expected to deviate from his strategy of confession, the outcome of the combined strategies (mutual confession) constitutes a Pareto inferior equilibrium.

A situation is defined as PD and generates the undesirable results noted above if the following inequalities among payoffs exist:

DC > CC > DD > CD

and 2CC > CD + DC.(39)

PD is by definition a non-cooperative game and communication is not allowed between the players. Yet even allowing the players to communicate would not significantly change the expected outcomes of the game. If the players could communicate, they would be expected to agree to adopt strategy CC to generate better …