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Cominetti, R., Quattropani, M., & Scarsini, M. (2022). The BuckPassing Game. Math. Oper. Res., Early Access.
Abstract: We consider two classes of games in which players are the vertices of a directed graph. Initially, nature chooses one player according to some fixed distribution and gives the player a buck. This player passes the buck to one of the player's outneighbors in the graph. The procedure is repeated indefinitely. In one class of games, each player wants to minimize the asymptotic expected frequency of times that the player receives the buck. In the other class of games, the player wants to maximize it. The PageRank game is a particular case of these maximizing games. We consider deterministic and stochastic versions of the game, depending on how players select the neighbor to which to pass the buck. In both cases, we prove the existence of pure equilibria that do not depend on the initial distribution; this is achieved by showing the existence of a generalized ordinal potential. If the graph on which the game is played admits a Hamiltonian cycle, then this is the outcome of priorfive Nash equilibrium in the minimizing game. For the minimizing game, we then use the price of anarchy and stability to measure fairness of these equilibria.

Rodriguez, R., NegretePincetic, M., Lorca, A., Olivares, D., & Figueroa, N. (2021). The value of aggregators in local electricity markets: A game theory based comparative analysis. SEGAN, 27, 100498.
Abstract: Demand aggregators are expected to have a key role in future electricity systems. More specifically, aggregators can facilitate the harnessing of consumers' flexibility. This paper focuses on understanding the value of the aggregator in terms of aggregation of both flexibility and information. We consider the aggregation of flexibility as the ability to exercise a direct control over loads, while the aggregation of information refers to knowledge of the flexibility characteristics of the consumers. Several game theory formulations are used to model the interaction between the energy provider, consumers and the aggregator, each with a different information structure. We develop a potential game to obtain the Nash equilibrium of the noncooperative game with complete information and we analyze the system dynamics of consumers using the adaptive expectations method in an incomplete information scenario. Several key insights about the value of aggregators are found. In particular, the value of the aggregator is mainly related to the aggregation of information rather than flexibility, and flexibility is valuable only when it can be coordinated. In this sense, prices are not enough to guarantee an effective coordination.
Keywords: Information; Flexibility; Potential game; Adaptive expectations method
