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Application of game theory in water resource management

Profile image of Simran JhawarSimran Jhawar

2018

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6 pages

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Abstract

With this research paper, we aim to analyse the effectiveness of Game Theory in Water Resource Allocation through simple twoby-two symmetric water resource games. The results of examples using three kinds of game theory icons are scanned to compare cooperative and non-cooperative game players. The highest payoff is achieved when both the players cooperate hence this paper explains how decision makers’ rational behaviour, who are trying to maximize their own objectives, might result in overall Pareto-inferior outcomes. Keywords— Game Theory, Prisoner’s Dilemma, Chicken game, Stag Hunt

Figures (2)
6.2 Chicken game aaa ama aii aia — haa In this game (Fig. 4) two drivers d riving a vehicle are heading towards a narrow bridge from opposite directions (they are drivin; towards each other). The first driver to swerve or ‘‘chicken” out yields the bridge to the other driver and loses. No driver enterin; the race wants to be the chicken, but if no driver chickens out, both drivers wil called a ‘‘chicken” is better than d ying but worse than winning, for both players tie, the players do not gain anything and the fight is over protecting their pride. they might both die proudly! The payoff of each player in this game can be the va from winning or losing the game. 1 two equilibria in which one driver loses and one driver wins, (DS, S) or (Win, Pareto-optimal. In the Chicken game, the strictly dominant strategy is to play exactly the opposite of what the other player does Similar to the Prisoner’s Dilemma suffer from the resulting crash. However, Bein; . A tie occurs when both players swerve. Under : If their pride are more important than their lives ue of the prize at the end of the game or the utilit The higher the payoff, the more preferred is the outcome (Madani, 2009). The Chicken game ha Lose) and (S, DS) or (Lose, Win), which are als game, each player wants to get a free ride and the cooperative or agreeable mutual solution ((S S) in Chicken and (DC, DC) in Prisoner’s Dilemma) is not stable since each player is willing to refrain from it. However, these tw games differ in that if both players decide to get free ride, the resulting outcome is the worst for both players in Chicken (DS, DS) (fi: 3) while the resulting outcome in Prisoner’s Dilemma (C, C) is suboptimal. but not the worst for both players. JTUWED OUT Cl Ube, LILLE MULLONLUE JUUP TO OF AUVOUNCO INO SCUNCHE UMU LICYVCLUPMeCrte crop sale revenues than the cases in which he decides to cooperate (Madani, 2009). On the other side, selecting a cooperative strategy while the other farmer is also willing to cooperate, results in the lowest payoff due to high pumping costs and low crop revenues (Madani, 2009). The optimal outcome of this game is (PR 1, PR 1) when both parties pump at the lower rate (Loaiciga, 2004). However, game theory suggests, each individual farmer finds the inferior PR 2 option as a strictly dominant strategy. Therefore, (PR 2, PR 2) is predicted outcome which is based on non-cooperative game theory and in fact such overpumping is typical for real unregulated aquifer systems. Lack of trust and cooperative strategy enforcement leads farmers to prefer pumping at the higher rate to increase short-run profits which are called ‘‘tragedy of the commons” (Hardin, 1968). Cooperation becomes harder with a lot of pumpers from the aquifer. In many water sharing problems around the world, non-cooperative behaviours of the player/parties have ed to “‘tragedy of the commons” outcomes despite the existence of cooperative solutions. Game theory explains and predicts such situations, even without precise quantitative information (fig 1 and fig 2). Thus, the results for any water resource problem with the same structure will be the same as in non-cooperative game theory where the ranking of the outcomes matters more than the actual payoff values associated with outcome (Madani, 2009). If the Prisoner’s Dilemma situation (game) is repeated more than few times, communication is allowed, and/or parties trust each other, the final resolution might be to cooperate (DC) to reach the Pareto-optimal resolution. Similarly, in water resources conflicts with a Prisoner’s Dilemma structure, explaining the problem to the parties and binding contracts (Madani, 2009) or other forms of trust might lead to cooperation and better solutions. Generally, in Prisoner’s Dilemma games, the threat of defection by other players results in non-cooperative behaviour. By understanding the structure of the game and by predicting (or interpreting) the players’ behaviours through game theory, it might be possible to find measures for enforcing better resolutions by changing the payoffs which change the structure of the game. For this groundwater game, if parties are assured that the extractions will be monitored and supervised by a regulating body and there is a penalty for defection from cooperation to non-cooperation, the defection threat is small, as non-cooperation is no longer a strictly dominant strategy. Carraro (Carraro, 2005) believe that many natural resource management issues have the characteristics of a Prisoner’s Dilemma game: players’ dominant strategy is not cooperative, and the resulting equilibrium is not Pareto-optimal. Similarly, most papers dealing with sharing natural resources problems have made the same assumption about the game to be the Prisoner’s Dilemma. However, not all common resource problems are Prisoner’s Dilemma (Sandler, 1992).
6.2 Chicken game aaa ama aii aia — haa In this game (Fig. 4) two drivers d riving a vehicle are heading towards a narrow bridge from opposite directions (they are drivin; towards each other). The first driver to swerve or ‘‘chicken” out yields the bridge to the other driver and loses. No driver enterin; the race wants to be the chicken, but if no driver chickens out, both drivers wil called a ‘‘chicken” is better than d ying but worse than winning, for both players tie, the players do not gain anything and the fight is over protecting their pride. they might both die proudly! The payoff of each player in this game can be the va from winning or losing the game. 1 two equilibria in which one driver loses and one driver wins, (DS, S) or (Win, Pareto-optimal. In the Chicken game, the strictly dominant strategy is to play exactly the opposite of what the other player does Similar to the Prisoner’s Dilemma suffer from the resulting crash. However, Bein; . A tie occurs when both players swerve. Under : If their pride are more important than their lives ue of the prize at the end of the game or the utilit The higher the payoff, the more preferred is the outcome (Madani, 2009). The Chicken game ha Lose) and (S, DS) or (Lose, Win), which are als game, each player wants to get a free ride and the cooperative or agreeable mutual solution ((S S) in Chicken and (DC, DC) in Prisoner’s Dilemma) is not stable since each player is willing to refrain from it. However, these tw games differ in that if both players decide to get free ride, the resulting outcome is the worst for both players in Chicken (DS, DS) (fi: 3) while the resulting outcome in Prisoner’s Dilemma (C, C) is suboptimal. but not the worst for both players. JTUWED OUT Cl Ube, LILLE MULLONLUE JUUP TO OF AUVOUNCO INO SCUNCHE UMU LICYVCLUPMeCrte crop sale revenues than the cases in which he decides to cooperate (Madani, 2009). On the other side, selecting a cooperative strategy while the other farmer is also willing to cooperate, results in the lowest payoff due to high pumping costs and low crop revenues (Madani, 2009). The optimal outcome of this game is (PR 1, PR 1) when both parties pump at the lower rate (Loaiciga, 2004). However, game theory suggests, each individual farmer finds the inferior PR 2 option as a strictly dominant strategy. Therefore, (PR 2, PR 2) is predicted outcome which is based on non-cooperative game theory and in fact such overpumping is typical for real unregulated aquifer systems. Lack of trust and cooperative strategy enforcement leads farmers to prefer pumping at the higher rate to increase short-run profits which are called ‘‘tragedy of the commons” (Hardin, 1968). Cooperation becomes harder with a lot of pumpers from the aquifer. In many water sharing problems around the world, non-cooperative behaviours of the player/parties have ed to “‘tragedy of the commons” outcomes despite the existence of cooperative solutions. Game theory explains and predicts such situations, even without precise quantitative information (fig 1 and fig 2). Thus, the results for any water resource problem with the same structure will be the same as in non-cooperative game theory where the ranking of the outcomes matters more than the actual payoff values associated with outcome (Madani, 2009). If the Prisoner’s Dilemma situation (game) is repeated more than few times, communication is allowed, and/or parties trust each other, the final resolution might be to cooperate (DC) to reach the Pareto-optimal resolution. Similarly, in water resources conflicts with a Prisoner’s Dilemma structure, explaining the problem to the parties and binding contracts (Madani, 2009) or other forms of trust might lead to cooperation and better solutions. Generally, in Prisoner’s Dilemma games, the threat of defection by other players results in non-cooperative behaviour. By understanding the structure of the game and by predicting (or interpreting) the players’ behaviours through game theory, it might be possible to find measures for enforcing better resolutions by changing the payoffs which change the structure of the game. For this groundwater game, if parties are assured that the extractions will be monitored and supervised by a regulating body and there is a penalty for defection from cooperation to non-cooperation, the defection threat is small, as non-cooperation is no longer a strictly dominant strategy. Carraro (Carraro, 2005) believe that many natural resource management issues have the characteristics of a Prisoner’s Dilemma game: players’ dominant strategy is not cooperative, and the resulting equilibrium is not Pareto-optimal. Similarly, most papers dealing with sharing natural resources problems have made the same assumption about the game to be the Prisoner’s Dilemma. However, not all common resource problems are Prisoner’s Dilemma (Sandler, 1992).
7. CONCLUSION In this example, let’s assume that 10 is the highest payoff, 5 is a lower payoff and 1 is the least payoff. Now, payoffs for both (A, B) will be: Same theory can provide insights to understand and resolve water conflicts which often are multi-criteria multi-decision-makers sroblems (Madani, Game theory and water resources, 2009). It sometimes can show and address different engineer-ing, socio- sconomic, and political characteristics of water resource problems even without detailed quantitative information and without a 1eed to express performances in conventional economic, financial, and physical terms (Madani, 2009). Game theory can predict if he Opti-mal resolutions are attainable and explain the decision makers’ behaviour under specific conditions. The stakeholders’ C) INTR www TTARNYD) rnm AI] Richte Rocverved Pooo | 7
7. CONCLUSION In this example, let’s assume that 10 is the highest payoff, 5 is a lower payoff and 1 is the least payoff. Now, payoffs for both (A, B) will be: Same theory can provide insights to understand and resolve water conflicts which often are multi-criteria multi-decision-makers sroblems (Madani, Game theory and water resources, 2009). It sometimes can show and address different engineer-ing, socio- sconomic, and political characteristics of water resource problems even without detailed quantitative information and without a 1eed to express performances in conventional economic, financial, and physical terms (Madani, 2009). Game theory can predict if he Opti-mal resolutions are attainable and explain the decision makers’ behaviour under specific conditions. The stakeholders’ C) INTR www TTARNYD) rnm AI] Richte Rocverved Pooo | 7

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