Shared Intentions & Game Theory

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.

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.

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 k  for which equilibria are k-strong).

Read the full paper here.

Watercooler chat, organizational structure and corporate culture by Newton, Wait and Angus, just released as a working paper.

Abstract:
Modeling firms as networks of employees, occasional collaborative decision making around the office watercooler changes long run employee behavior (corporate culture). The culture that emerges in a given team of employees depends on team size and on how the team is connected to the wider firm. The implications of the model for organizational design are explored and related to empirical research on communication, innovation, the size and decision making of corporate boards and trends in the design of hierarchical structures.

“Stochastic stability in assignment problems“, by Klaus and Newton, just published in the Journal of Mathematical Economics.

Check out the summary of existing literature on the emergence of norms in matching problems at sharedintentions.net.

Simon Angus appeared today on ABC’s Radio National – Afternoons, hosted by Michael Mackenzie, to discuss joint work with Jonathan Newton recently published in PLoS Computational Biology (and featured on this site here).

The discussion mostly focused on the background to the paper — namely the Vygotskian intelligence hypothesis of Michael Tomasello and others, and his recent research that aims to illicit the key cognitive differences between human infants and related apes in settings in which the hall-marks of shared intentionality might be expected to arise.

You can download or listen to the discussion here.

“Emergence of Shared Intentions is Coupled to the Advance of Cumulative Culture“, by Angus and Newton, just published at PLoS Computational Biology.

Check out the video at the study’s page right here on sharedintentions.net.

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