Aggregation in Game Theoretical Situations

The thesis deals with the class of Aggregative Games, namely strategic form games where each payoff function depends on the corresponding player's strategy and on some aggregation among strategies of all involved players. The first part of the thesis is devoted to the multi-leader multi-follower equilibrium concept for the class of aggregative games: the considered game presents aymmetry between two groups of players, acting noncooperatively within the group and one group is the leader in a leader-follower hierarchical model. Moreover, as it happens in concrete situations, the model is affected by uncertainty and the game is considered in a stochastic context. Assuming an exogenous uncertainty affecting the aggregator, the multi-leader multi-follower equilibrium model is presented and existence results for the stochastic resulting game are obtained in the smooth case of nice aggregative games, where payoff functions are continuous and concave in own strategies, as well as in the general case of aggregative games with strategic substitutes. These results apply to the global emission game and the teamwork project game. Then, an investment in Common-Pool Resources is studied: the situation of many agents interested in a common-pool resource, like water resource, is modeled as an aggregative game and existence results of Nash equilibria are obtained with or without convexity-like assumptions. In the special case of quadratic return functions, the game is also considered under uncertainty i.e. when the possibility of a natural disaster with a given probability may occur. In the second part of the thesis, in line with the literature on additively separable aggregative games, a class of non cooperative games, called Social Purpose Games, is introduced. In this class of games the payoff of each player depends separately on his own strategy and on a function of the strategy profile, the aggregation function, which is the same for all players, weighted by an individual benefit parameter which enlightens the asymmetry between agents toward the social part of the benefit. The two parts of the payoff function represent respectively the individual and the social benefits. For the class of social purpose games it has been showed that they have a potential, providing also a comparison between the Nash equilibrium strategies and the social optimum strategies, namely when all the players agree in maximizing the aggregate profit. For social purpose games we study the existence of the so called coalition leadership equilibrium: it is a multi-leader multi-follower model where a cooperative behaviour is assumed between players of the leading group and they decide to maximize the aggregation of their payoffs. The rest of the players act noncooperatively. This kind of equilibrium presents a mixture of cooperative and noncooperative behaviour, situation that often occurs in many applicative examples. The weights affecting the aggregation function allow to derive explicit conditions under which the leading coalition is stable. An application to a water resource game is illustrated

Quantity Competition, Endogenous Motives and Behavioral Heterogeneity

The paper shows that strategic quantity competition can be characterized by behavioral heterogeneity, once competing firms are allowed in a pre-market stage to optimally choose the behavioral rule they will follow in their strategic choice of quantities. In particular, partitions of the population of identical firms in profit maximizers and relative profit maximizers turn out to be deviation-proof equilibria, both in simultaneous and sequential game structures. Our findings that in a strategic framework heterogeneous behavioral rules are consistent with individual incentives provides a game-theoretic microfoundation of heterogeneity.Behavioral Heterogeneity, Endogenous Motives, Relative Performance, Multistage Games, Quantity Competition.

Games without winners: Catching-up with asymmetric spillovers

Dynamic game with changing leader is studied on the example of R&D co-opetition structure. The leader benefits from higher followers' innovations rate and followers are enjoying a spillover from the leader. Leadership changes because of asymmetric efficiency of investments of players. It is demonstrated that under sufficiently asymmetric players there is no long-run leader in this game and all players act as followers. Moreover this outcome may be the socially optimal one. In decentralised setting additional complex types of dynamics are observed: permanent uctuations around symmetric (pseudo)equilibrium and chaotic dynamics. This last is possible only once strategies of players are interdependent. Cooperative solution is qualitatively similar for any number of players while market solution is progressively complex given all players are asymmetric. Results are extended to an arbitrary linear-quadratic multi-modal differential game with spillovers and the structure necessary for the onset of non-deterministic chaos is discussed

GAME THEORETIC FLOW AND ROUTING CONTROL FOR COMMUNICATION NETWORKS

As the need to support high speed data exchange in modern communication networks grows rapidly, effective and fair sharing of the network resources becomes very important. Today's communication networks typically involve a large number of users that share the same network resources but may have different, and often competing, objectives. Advanced network protocols that are implemented to optimize the performance of such networks typically assume that the users are passive and are willing to accept compromising their own performance for the sake of optimizing the performance of the overall network. However, considering the trend towards more decentralization in the future, it is natural to assume that the users in a large network may take a more active approach and become more interested in optimizing their own individual performances without giving much consideration to the overall performance of the network. A similar situation occurs when the users are members of teams that are sharing the network resources. A user may find itself cooperating with other members of its team which itself is competing with the other teams in the network. Game theory appears to provide the necessary framework and mathematical tools for formulating and analyzing the strategic interactions among users, or teams of users, of such networks. In this thesis, we investigate networks in which users, or teams of users, either compete or cooperate for the same network resources. We considered two important network topologies and used many examples to illustrate the various solution concepts that we have investigated.. First we consider two-nodeiiiparallel link networks with non-cooperative users trying to optimally distribute their flows among the links. For these networks, we established a condition which guarantees the existence and uniqueness of a Nash equilibrium for the link flows. We derived an analytical expression for the Nash equilibrium and investigated its properties in terms of the network parameters and the users preferences. We showed that in a competitive environment users can achieve larger flow rates by properly emphasizing the corresponding term in their utility functions, but that this can only be done at the expense of an increase in the expected delay. Next, we considered a general network structure with multiple links, multiple nodes, and multiple competing users. We proved the existence of a unique Nash equilibrium. We also investigated many of its intuitive properties. We also extended the model to a network where multiple teams of users compete with each other while cooperating within the teams to optimize a team level performance. For this model, we studied the Noninferior Nash solution and compared its results with the standard Nash equilibrium solution

Integrated game-theory modelling for multi enterprise-wide coordination and collaboration under uncertain competitive environment

In this work, an integrated Game Theory (GT) approach is developed for the coordination of multi-enterprise Supply Chains (SCs) in a competitive uncertain environment. The conflicting goals of the different participants are solved through coordination contracts using a non-cooperative non-zero-sum Stackelberg game under the leadership of the manufacturer. The Stackelberg payoff matrix is built under the nominal conditions, and then evaluated under different probable uncertain scenarios using a Monte-Carlo simulation. The competition between the Stackelberg game players and the third parties is solved through a Nash Equilibrium game. A novel way to analyze the game outcome is proposed based on a win–win Stackelberg set of “Pareto-frontiers”. The benefits of the resulting MINLP tactical models are illustrated by a case study with different vendors around a client SC. The results show that the coordinated decisions lead to higher expected payoffs compared to the standalone case, while also leading to uncertainty reduction.Peer ReviewedPostprint (author's final draft