Cost Sharing Models in Game Theory = Költségelosztási modellek a játékelméletben

Kivonat, rövid leírás

In our thesis we examined economic situations modeled with rooted trees and directed, acyclic graphs. In the presented problems the collaboration of economic agents (players) incurred costs or created a profit, and we have sought answers to the question of \fairly" distributing this common cost or profit. We have formulated properties and axioms describing our expecta- tions of a \fair" allocation. We have utilized cooperative game theoretical methods for modeling. After the introduction, in Chapter 2 we analyzed a real-life problem and its possible solutions. These solution proposals, namely the average cost- sharing rule, the serial cost sharing rule, and the restricted average cost- sharing rule have been introduced by Aadland and Kolpin (2004). We have also presented two further water management problems that arose during the planning of the economic development of Tennessee Valley, and discussed solution proposals for them as well (Straffinn and Heaney, 1981). We analyzed if these allocations satisfied the properties we associated with the notion of \fairness". In Chapter 3 we introduced the fundamental notions and concepts of cooperative game theory. We defined the core (Shapley, 1955; Gillies, 1959) and the Shapley value (Shapley, 1953), that play an important role in finding a \fair" allocation. In Chapter 4 we presented the class of fixed-tree game and relevant ap- plications from the domain of water management. In Chapter 5 we discussed the classes of airport and irrigation games, and the characterizations of these classes. We extended the results of Dubey (1982) and Moulin and Shenker (1992) on axiomatization of the Shapley value on the class of airport games to the class of irrigation games. We have \translated" the axioms used in cost allocation literature to the axioms corresponding to TU games, thereby providing two new versions of the results of Shapley (1953) and Young (1985). In Chapter 6 we introduced the upstream responsibility games and char- acterized the game class. We have shown that Shapley's and Young's char- acterizations are valid on this class as well. In Chapter 7 we discussed shortest path games and have shown that this game class is equal to the class of monotone games. We have shown that further axiomatizations of the Shapley value, namely Shapley (1953)'s, Young (1985)'s, Chun (1989)'s, and van den Brink (2001)'s characterizations are valid on the class of shortest path games.