We provide a game-theoretic analysis of consensus, assuming that processes are controlled by rational agents and may fail by crashing. We consider agents that care only about consensus: that is, (a) an agent's utility depends only on the consensus value achieved (and not, for example, on the number of messages the agent sends) and (b) agents strictly prefer reaching consensus to not reaching consensus. We show that, under these assumptions, there is no ex post Nash Equilibrium, even with only one failure. Roughly speaking, this means that there must always exist a failure pattern (a description of who fails, when they fail, and which agents they do not send messages to in the round that they fail) and initial preferences for which an agent can gain by deviating. On the other hand, if we assume that there is a distribution π on the failure patterns and initial preferences, then under minimal assumptions on π, there is a Nash equilibrium that tolerates f failures (i.e., π puts probability 1 on there being at most f failures) if f + 1 < n (where n is the total number of agents). Moreover, we show that a slight extension of the Nash equilibrium strategy is also a sequential equilibrium (under the same assumptions about the distribution π).

Abstract. Community network clouds provide for applications of local interest deployed within community networks through collaborative efforts to provision cloud infrastructures. They complement the traditional large-scale public cloud providers similar to the model of decentralised edge clouds by bringing both content and computation closer to the users at the edges of the network. Services and applications within community network clouds require connectivity to the Internet and to the resources external to the community network, and here the current besteffort model of volunteers contributing gateway access in the community networks falls short. We model the problem of reserving the bandwidth at such gateways for guaranteeing quality-of-service for the cloud applications, and evaluate different pricing mechanisms for their suitability in ensuring maximal social welfare and eliciting truthful requests from the users. We find second-price auction based mechanisms, including Vickrey and generalised second price auctions, suitable for the bandwidth allocation problem at the gateways in the community networks.

This work uses Game Theory to study the effectiveness of punishments as an incentive for rational nodes to follow an epidemic dissemination protocol. The dissemination process is modeled as an infinite repetition of a stage game. At the end of each stage, a monitoring mechanism informs each player of the actions of other nodes. The effectiveness of a punishing strategy is measured as the range of values for the benefit-to-cost ratio that sustain cooperation. This paper studies both public and private monitoring. Under public monitoring, we show that direct reciprocity is not an effective incentive, whereas full indirect reciprocity provides a nearly optimal effectiveness. Under private monitoring, we identify necessary conditions regarding the topology of the graph in order for punishments to be effective. When punishments are coordinated, full indirect reciprocity is also effective with private monitoring.