GAME THEORY AND TRANSBOUNDARY IVER MANAGMENT: A THEORETICAL BACK GROUND

di

 Federico Salvati

 (federicoslvt@gmail.com)

Water is a vital  for human life but not everywhere this essential asset is abundant. For this reason, sadly, many community are force to administrate the water in order to maximize the utility and to not squander the already scarce asset. Water management is one of the main strategical issues of our times. In some regions like central Asia or North Africa the topic affect  the daily life of millions of people in a scenario where the human life is still irremediably bound to the geographical datum. When the resource is shared by tow or more state the situation can rise strategic competition and water management become even a more thorny argument. A shared river basin at the same time can be source of fierce wars or steady cooperation. In order to analyze the scenario we can use a game theory approach. This perspective allows us to conceptualize main interests and their related behavior forecasting probable outcomes and choices. The big flaw of this approach is that we assume the actors to be completely rational. Many aspects which belong to the cultural or the social- anthropological sphere are not taken in account, even though empirically they can have a major influence depending by the case. Furthermore in many analysis it is not clear upon what basis the pay-offs of the games calculated. This can create arbitrary assumption that can affect the analysis from its very basics. Theoretically speaking anyway hardly social science has found an as valid approach as game theory is. According to such analysis the central focus has to be posed on externalities problems. When an upstream country decide to use a transboundary river course it creates externalities for the downstream state manipulating either the quality and the quantity of the resource. Seen the premises the fallowing question now is to explain how and if these externalities can be internalized and what would be the consequences of the different available strategies. Non- cooperative game models for this specific scenario seem to fit pretty well. According to non- cooperative game theory the parties are engaged in a competitive strategic relation. They will try to maximize their behaviour by choosing their strategies. The players are interconnected and: every decision of one party will affect possibility and strategy of the other. Non -cooperative strategy (E.G. prisoner dilemma strategy) tends to not generate cooperation between the parties, since the risk of been exploited is too high. In a classical non cooperative game the players will go for a non cooperative strategy which is strictly dominant on the cooperative one, reaching so their Nash equilibrium.

FIG. 1 Classical prisoner dilemma

                                                              COOP            EXPLOIT

1            1	3         -3
-3             3	0          0

We can recognize in this game the classical prisoner dilemma structure.

A general solution for the prisoner dilemma is to repeat the single game. The repetition makes rationally a better strategy to cooperate since it is the only manner to maximize the pay-off. The equilibrium in the long term can differ from the equilibrium in the subgame. Fundamental assumption remains that such repetition (as in the case of transboundary river management ) it doesn't have and end game. In the opposite case a strict domination for the non-cooperation strategy would be recreated in the endgame and cooperation will fail. Another important circumstance to analyze is the possibility for the down stream country to improve its bargain power by linking different issues together. In this case the new equilibrium for the game would be found in a mixed matrix interlinking all the issues. In the shared river basin scenario we can easily an bright example of it. The upstream country acting unilaterally in the river exploitation can generate a security dilemma-like situation. By increasing its welfare the upstream country will decease the downstream one. This will generate instability and insecurity, creating border troubles and problems akin. Bluntly put if we deprive the downstream country of all the water indirectly we will generate a security problem between the tow actors. In the mixed game example the upstream and the downstream country can find new equilibrium, choosing a strategy more profitable for both actors. More simply reworded by giving up a bit in one issue they will receive an upper pay-off gaining more from the other .

fig. 2 mixed game

                                                    coop           coop    explo           explo

                                                    instability  secu     secu           instability                      

5          2	-1           3	1         2.5	-5           3.5
6          0	4           3	2         0.5	-2           1.5
4          0	-2           1	3           1	-3           2
5        -2	1           1	4         -1	0           0

The possibility to find a better solution to the game by multiplying interests is backed up also by another game theory feature. We assume usually that a government has more targets than means to achieve them. They have therefore to trade-off in order to achieve what they can, with what they have. This will make coordination more likely to happen and more important. This kind of thinking brings up more questions then answers. For example we can discuss about what is the extent of the trade off or what are the endogenous mechanisms that push the decision-makers to stand for a specific goal. Anyway one think certainly remains: the actors in a regional environment if they have a trade-off situation (like water-security ), they can have higher out-comes when they cooperate. Such a situation has found vast proof (analytically and empirically) thanks to the works of economists like Hamada, Ghosh and Masson.

Fig 3 cooperation game

                                                                  EXPLOIT   COOP

                                                          

0        0	0          0
0         0	1          1

Under this prospective we can use a different kind of approach to describe the problem. Let us assume in this case the existence of a cooperative game. According to the cooperative game theory the  members will have to seek coordination. The pay-off are more higher when the parties coordinate. If they don't do so they will face added costs or simply lower out- comes. In the water management case this is clearly relevant. Thinking our case in a dynamic perspective, according to the perspective of a cooperative game there is an astounding result. In fact by cooperating the cost faced by one of the parties in a specific field will yield an increase of utility over the fact per se. Generation of positive externalities will produce a snowballing effect where the action will have a final utility which comprehends at the same time the value per se of the action plus the avoidance of further problem creation. In our specific case for instance we can present as a case in point security issues. If the upstream country pumped all the water for its purposes, the downstream country would be left without the wherewithal for feeding the population. This would generate a commitment problem. The downstream country has to take control of the river basin because otherwise the population will starve to death. By finding an efficient mean to prevent starvation of the downstream country the upstream country could have, for instance, electricity production, plus the prevention of a military attack. As we said in the introduction game theory is not a perfect tool of analysis. Models are just a exemplification of real life but we can hardly find a similar tool that give as such a challenging frame for setting our reasoning

 (geografia2013@libero.it)