Fresh SI: The evolution of collaboration in symmetric 2×2-games with imperfect recognition of types

In a recent paper published in Games and Economic Behavior, Hannes Rusch considers the evolution of collaboration. That is, he asks in what circumstances the ability to create shared intentions and undertake collaborative action choice can proliferate.

Previous work on this topic (see our discussion here) has considered the operation of group selection (Angus & Newton, 2015) or analyzed the complexities that arise from positive and negative externalities of collaboration on third parties (Newton, 2017).

The paper under discussion differs from prior work in that players with the ability to collaborate imperfectly recognize whether or not others have the ability to collaborate. For example, Alice may have the ability to collaborate, and may erroneously think that Bob also has the ability.

Alice may then see a large animal and say “Hey Bob, let’s hunt that animal!”, thinking that Bob will fulfill his role in a hunt. When Bob fails to adequately carry out this role, it may turn out that Alice would have been better off not hunting at all.

Read the full paper here.

Fresh SI: Stochastic stability under logit choice in coalitional bargaining problems

In a recent paper published in Games and Economic Behavior, Ryoji Sawa considers the emergence of distributive norms in situations in which surplus is produced by coalitions of players.

Previous work (Newton, 2012 – discussed here) found that if strategy updating takes place under a coalitional dynamic with uniform probabilities of a “mistake” (a non-best response), then in the long run there is a tendency towards Rawlsian social choice – the emergence of social norms that maximize the wealth of the poorest members of society.

In contrast, Sawa uses the coalitional logit choice rule (Sawa, 2014 – discussed here) and finds the emergence of social norms that minimize the wealth of the richest members of society. This is similar to the finding of Agastya (1999, see link together with a general discussion of the Evolutionary Nash Program here). However, Agastya’s model used uniform mistakes in an individualistic dynamic. Therefore, two models that differ in these two aspects (perturbation structure and presence or absence of SI) lead to similar outcomes.

Read the full paper here.

Fresh ENP: Conventional contracts, intentional behavior and logit choice: equality without symmetry

In a new paper in the Evolutionary Nash Program published in Games and Economic Behavior, Sung-Ha Hwang, Wooyoung Lim, Philip Neary and Jonathan Newton show how egalitarianism can emerge in asymmetric environments.

Specifically, when coordination games are played under the logit choice rule and there is intentional bias in agents’ non-best response behavior, the Egalitarian bargaining solution emerges as the long run social norm. Without intentional bias, a new solution, the Logit bargaining solution emerges as the long run norm.

These results contrast with results under non-payoff dependent deviations from best response behavior, where it has previously been shown that the Kalai–Smorodinsky and Nash bargaining solutions emerge as long run norms.

Experiments on human subjects, reported in the paper, suggest that non-best response play is payoff dependent and displays intentional bias. This suggests the Egalitarian solution as the most likely candidate for a long run bargaining norm.

Read the full paper here. Read more on the Evolutionary Nash Program on this site here.

Fresh SI: Agency Equilibrium

In a recent working paper, Jonathan Newton gives a fixed point solution concept that incorporates collective agency under incomplete information.

In keeping with the ethos of the SI project, agency may be exercised by different entities (e.g. individuals, firms, households). A given individual can form part of multiple agents (e.g. he may belong to a firm and a household).

However, the set of agents that act in a given situation might not be common knowledge. For example, Alice may not know whether Bob and Colm have formed a coalition and constitute a collective agent.

The paper models such considerations, inspired by the classic model of incomplete information over preferences of Harsanyi.

Read the full paper here.

Fresh SI: Newton & Sercombe on agency, potential and contagion

In a recent working paper, Jonathan Newton and Damian Sercombe consider the relationship between the aggregation of incentives at the individual level (using the mathematical tool of a potential function) and the aggregration of agency in decision making.

They find that the relationship between incentives and agency is related in striking ways to the payoffs of the underlying game they consider.

Results are proven by showing relationships between the pre-existing graph theoretic concepts of the close-knittedness and cohesion of sets of players whose interaction is mediated by a graph.

Read the full paper here.

Fresh SI: Newton on the evolution of collaboration

The ability to form shared intentions and adjust one’s choices in collaboration with others is a fundamental aspect of human nature.

In a recent publication in Games and Economic Behavior, Jonathan Newton discusses the forces that act for and against the evolution of this ability.

In contrast to altruism and other non-fitness maximizing preferences, for large classes of games the ability to form shared intentions and undertake collaborative activity proliferates when rare without requiring group selection or assortativity in matching.

Read the full paper here.

Fresh SI: Okada & Sawa on the implications of collective agency arising from majority voting

In a new working paper, Akira Okada and Ryoji Sawa examine an evolutionary model in which the policy followed by a collective is determined by majority (or supermajority) voting by individuals. They look at the kind of policies that emerge under given voting rules.

A voting rule can be considered a way of forming a collective intention. In fact, it can be a strong way of forming a collective intention as the wishes of individuals in a minority are disregarded. It follows that, in this sense, the weakest voting rule is the one that requires ALL individuals to agree: the unanimity voting rule.

Under the unanimity rule, the only way a new policy x can defeat a status quo policy y is if every individual voting weakly prefers x to y. This is exactly the Coalitional Better Response rule found in Newton and Angus (2015, paper, video).

Okada and Sawa find that when their voting dynamic is perturbed uniformly, in the long run Condorcet winning  policies tend to emerge. When perturbations depend on payoffs (specifically, logit) Borda winning policies tend to emerge.

For more, see the paper.

Fresh SI: Nax and Perc on the replication of coalitionally beneficial behaviour by individual mistakes

In this paper published in Scientific Reports, Heinrich Nax and Matjaz Perc discuss naive learning in public goods games. They examine a situation in which simultaneous mistakes by multiple players can end up benefiting the mistake making players. For example, it could be the case that 3 players make mistakes and play a myopically suboptimal action, but that because they make mistakes simultaneously they gain payoff from these mistakes.

Hence, profitable coalitional moves are replicated by the mistakes of individuals. To replicate coalitional moves by larger numbers of players will require a larger number of mistakes and so such moves will be relatively less likely. This is similar to the assumption made in Newton (2012, paper, web), although in the cited paper it is an assumption, whereas in Nax and Perc it emerges endogeneously as described above.

A Nash equilibrium is k-strong if there exists no profitable coalitional deviation for a coalition of any size up to and including k  (see the paper under discussion or Newton & Angus, 2013). The authors show that behaviour under naive learning depends on the k-strength of the equilibria in their model (i.e. on the value of for which equilibria are k-strong).

Read the full paper here.