The Shapley Value in the Knaster Gain Game

In Briata, Dall'Aglio and Fragnelli (2012), the authors introduce a coopera- tive game with transferable utility for allocating the gain of a collusion among completely risk-averse agents involved in the fair division procedure introduced by Knaster (1946). In this paper we analyze the Shapley value (Shapley, 1953) of the game and propose its use as a measure of the players' attitude towards collusion. Furthermore, we relate the sign of the Shapley value with the ranking order of the players' evaluation, and show that some players in a given ranking will always deter collusion. Finally, we characterize the coalitions that maximize the gain from collusion, and suggest an ad-hoc coalition formation mechanism

Dynamic Collusion and Collusion Games in Knaster's Procedure

3noIn this paper we study the collusion in Knaster’s procedure, starting from the paper of Fragnelli and Marina (2009). First, we introduce a suitable dynamic mechanism, so that the coalition enlargement is always non-disadvantageous. Then, we define a new class of TU-games in order to evaluate the collusion power of the agents.openopenBriata, Federica; Dall'Aglio, Marco; Fragnelli, VitoBriata, Federica; Dall'Aglio, Marco; Fragnelli, Vit

In whose backyard? A generalized bidding approach

We analyze situations in which a group of agents (and possibly a designer) have to reach a decision that will affect all the agents. Examples of such scenarios are the location of a nuclear reactor or the siting of a major sport event. To address the problem of reaching a decision, we propose a one-stage multi-bidding mechanism where agents compete for the project by submitting bids. All Nash equilibria of this mechanism are efficient. Moreover, the payoffs attained in equilibrium by the agents satisfy intuitively appealing lower bounds..externalities, bidding, implementation

Dynamic Games under Bounded Rationality

I propose a dynamic game model that is consistent with the paradigm of bounded rationality. Its main advantages over the traditional approach based on perfect rationality are that: (1) under given state the strategy space is a chain-complete partially ordered set; (2) the response function satisfies certain order-theoretic property; (3) the evolution of economic system is described by the Dynamical System defined by iterations of the response function; (4) the existence of equilibrium is guaranteed by fixed point theorems for ordered structures. If the preference happens to be represented by a utility function and the response was derived from utility maximization, then the equilibrium defined by fixed points of the response function will be the same as Nash equilibrium. This preference-response framework liberates economics from the utility concept, and constitutes a synthesis between normal-form and extensive-form games. And the essential advantages of our preference-response approach was secured by successfully resolving some long-standing paradoxes in classical theory, yielding straightforward ways out of the impossibility theorem of Arrow and Sen, the Keynesian beauty contest, the Bertrand Paradox, and the backward induction paradox. These applications have certain characteristics in common: they all involve important modifications in the concept of perfect rationality

In whose backyard? A generalized bidding approach

We analyze situations in which a group of agents (and possibly a designer) have to reach a decision that will affect all the agents. Examples of such scenarios are the location of a nuclear reactor or the siting of a major sport event. To address the problem of reaching a decision, we propose a one-stage multi-bidding mechanism where agents compete for the project by submitting bids. All Nash equilibria of this mechanism are efficient. Moreover, the payoffs attained in equilibrium by the agents satisfy intuitively appealing lower bounds.

Quality-Of-Service Provisioning in Decentralized Networks: A Satisfaction Equilibrium Approach

This paper introduces a particular game formulation and its corresponding notion of equilibrium, namely the satisfaction form (SF) and the satisfaction equilibrium (SE). A game in SF models the case where players are uniquely interested in the satisfaction of some individual performance constraints, instead of individual performance optimization. Under this formulation, the notion of equilibrium corresponds to the situation where all players can simultaneously satisfy their individual constraints. The notion of SE, models the problem of QoS provisioning in decentralized self-configuring networks. Here, radio devices are satisfied if they are able to provide the requested QoS. Within this framework, the concept of SE is formalized for both pure and mixed strategies considering finite sets of players and actions. In both cases, sufficient conditions for the existence and uniqueness of the SE are presented. When multiple SE exist, we introduce the idea of effort or cost of satisfaction and we propose a refinement of the SE, namely the efficient SE (ESE). At the ESE, all players adopt the action which requires the lowest effort for satisfaction. A learning method that allows radio devices to achieve a SE in pure strategies in finite time and requiring only one-bit feedback is also presented. Finally, a power control game in the interference channel is used to highlight the advantages of modeling QoS problems following the notion of SE rather than other equilibrium concepts, e.g., generalized Nash equilibrium.Comment: Article accepted for publication in IEEE Journal on Selected Topics in Signal Processing, special issue in Game Theory in Signal Processing. 16 pages, 6 figure