Coordination on networks with farsighted and myopic agents

We study a coordination game on a fixed connected network where players have to choose between two projects. Some players are moderate (i.e. they are ex-ante indifferent between both projects) while others are stubborn (i.e. they always choose the same project). Benefits for moderate players are increasing in the number of neighbors who choose the same project. In addition, players are either farsighted or myopic. Farsighted players anticipate the reactions of others while myopic players do not. We show that, when all players are farsighted, full coordination among the moderate players is reached except if there are stubborn players for both projects. When the population is mixed, the set of stable strategy profiles is a refinement of the set of Nash equilibrium strategy profiles. In fact, turning myopic players into farsighted ones eliminates gradually the inefficient Nash equilibria. Finally, we consider a social planner who can improve coordination by means of two policy instruments: adding links to the network (socialization) and/or turning myopic players into farsighted ones (education).

Coordination and Equilibrium Selection in Games: The Role of Local Effects

We study the role of local effects and finite size effects in reaching coordination and in equilibrium selection in two-player coordination games. We investigate three update rules – the replicator dynamics (RD), the best response (BR), and the unconditional imitation (UI). For the pure coordination game with two equivalent strategies we find a transition from a disordered state to coordination for a critical value of connectivity. The transition is system-size-independent for the BR and RD update rules. For the IU it is system-size-dependent, but coordination can always be reached below the connectivity of a complete graph. We also consider the general coordination game which covers a range of games, such as the stag hunt. For these games there is a payoff-dominant strategy and a risk-dominant strategy with associated states of equilibrium coordination. We analyse equilibrium selection analytically and numerically. For the RD and BR update rules mean-field predictions agree with simulations and the risk-dominant strategy is evolutionary favoured independently of local effects. When players use the unconditional imitation, however, we observe coordination in the payoff-dominant strategy. Surprisingly, the selection of pay-off dominant equilibrium only occurs below a critical value of the network connectivity and disappears in complete graphs. As we show, it is a combination of local effects and update rule that allows for coordination on the payoff-dominant strategy.

Delegation Using Forward Induction

This paper explores how delegation can be used as a signal to sustain cooperation. I consider a static principal–agent model with two tasks, one resembling a coordination game. If there is asymmetric information about the agent’s type, the principal with high private belief can delegate the first task as a signal. This is also supported by the forward induction argument. However, in the laboratory setting, this equilibrium is chosen only sometimes. When the subjects have information about past sessions, there is a significant increase in the use of delegation. This finding sheds light on equilibrium selection in Bayesian games.

Modelling Virtual Bargaining using Logical Representation Change

We discuss work in progress on the computational modelling of virtual bargaining: inference-driven human coordination under severe communicative constraints. For this initial work we model variants of a two-player coordination game of item selection and avoidance taken from the current virtual bargaining literature. In this range of games, human participants collaborate to select items (e.g. bananas) or avoid items (e.g. scorpions), based on signalling conventions constructed and updated from shared assumptions, with minimal information exchange. We model behaviours in these games using logic programs interpretable as logical theories. From an initial theory comprised of rules, background assumptions and a basic signalling convention, we use automated theory repair to jointly adapt that basic signalling convention to novel contexts, with no explicit coordination between players. Our ABC system for theory repair delivers spontaneous adaptation, using reasoning failures to replace established conventions with better alternatives, matching human players’ own reasoning across several games.

Meeting and Missing Minds: Children and Adults Use Alignment of Intuitions to Solve Pure Coordination Games

In pure coordination games players seek to coordinate responses with one another without communicating. Without a logically correct response, success depends upon players intuiting a response that is mutually obvious. Previous work suggests that such coordination requires a distinctive form of “group” thinking and sufficient mutual knowledge, but reveals little about the basis for the intuitive judgements themselves. Here, that question was addressed for the first time by examining the basis of coordination performance of groups whose intuitions might plausibly differ: children versus adults. Twenty-five 5-year-olds, 30 7-year-olds, and 25 adults undertook four types of coordination game, and novel metrics allowed “intuitive alignment” in responses to be evaluated within- and between-groups. All groups performed above chance, and adults showed higher levels of alignment than children, but adults and children showed different patterns in their intuitions. Implications for intergenerational understanding and mis-understanding are discussed.

Coordination games in cancer

We propose a model of cancer initiation and progression where tumor growth is modulated by an evolutionary coordination game. Evolutionary games of cancer are widely used to model frequency-dependent cell interactions with the most studied games being the Prisoner's Dilemma and public goods games. Coordination games, by their more obscure and less evocative nature, are left understudied, despite the fact that, as we argue, they offer great potential in understanding and treating cancer. In this paper we present the conditions under which coordination games between cancer cells evolve, we propose aspects of cancer that can be modeled as results of coordination games, and explore the ways through which coordination games of cancer can be exploited for therapy.

Voluntary redistribution mechanism in asymmetric coordination games

An inequality game is an asymmetric 2 × 2 coordination game in which player 1 earns a substantially higher payoff than player 2 except in the inefficient Nash equilibrium (NE). The two players may have either common or conflicting interests over the two NE. This paper studies a redistribution scheme which allows the players to voluntarily transfer their payoffs after the play of an inequality game. We find that the redistribution scheme induces positive transfer from player 1 to player 2 in both common- and conflicting- interest games, and is particularly effective in increasing efficient coordination and reducing coordination failures in conflicting-interest games. We explain these findings by considering reciprocity by player 1 in response to the sacrifice made by player 2 in achieving efficient coordination in conflicting-interest games.