Contra previous research [1,2], I show that communication is generically impossible between parties with precisely (statistically) independent interests if there is any uncertainty about the sender's preference. I propose that these earlier works should instead be interpreted as approximate descriptions of equilibria that occur when preferences are slightly dependent — e.g. if preferences are correlated because the sender feels slight empathy for the receiver.
Not every equilibrium can be interpreted in this way. I characterize the relationship between general state-dependence in the sender's preference and the equilibria that it robustly preserves.
This analysis centres on "communication graphs", a novel representation/classification of sender strategies. Our robustness criterion rules out cyclic communication graphs, which I show generically constrains equilibria to connected graphs. This property of connectedness prohibits separating equilibria.
We apply these techniques to show how increasing the alignment between parties' preferences is beneficial in settings where actions are 'horizontally differentiated', but can impede communication when actions are 'vertically differentiated'. In the latter setting money-burning can significantly benefit a sender with slightly state-dependent preferences, despite not benefitting a sender with state-independent preferences.
I model a large anonymous society where individuals repeatedly face a dilemma between acting selfishly or contributing to social surplus (à la Prisoner's Dilemma). If agents care even slightly about the social surplus then pro-social norms can be sustained through a desire to set an example for others.
In contrast to other models of cooperation in this setting, this mechanism supports partial norms (followed by only a portion of society) and functions independent of population size (classic mechanisms require arbitrarily large patience [1]).
Enriching the model by adding private/public agent characteristics, the model predicts that pro-social norms are unsustainable in more unequal societies as well as poorly integrated societies.
*This is a follow-up to the Robust Communication paper.
In practice the precise relationship between incentives and communication is unclear: How much profit needs to be at stake for a lobbyist to be willing to mislead a policymaker? How much value does an undergraduate degree need to bring a student before they are willing to enrol? Nevertheless the directional relationship of incentives is often clear: lobbyists are more willing to deceive if the profit at stake is higher, more skilled students are more willing to enrol in a degree.
We propose a minimalist model of communication centred around two ordinal components of preferences: a state-independent monotonicity component (e.g. higher profit is better), and the relative biases (e.g. skilled students are biased towards schooling). The sender's preference is otherwise known.
The role of these ordinal components can be separated in our analysis.
Is anything lost by ignoring small heterogeneities when analyzing a game?
Harsanyi's purification theorem [1, wikipedia] answers this question "Generically, no." showing that for generic games the only effect of slight heterogeneities is to 'purify' mixed strategy equilibria. However, theorists often find their way into this measure-0 set of games through natural assumptions (examples include cheap talk, repeated games, Abreu-Gul bargaining without behavioural agents).
I aim to explain that purification fails when an equilibrium exploits "strategic redundancies" and invariances of a game. Equilibrium selection techniques often serve to remove these redundancies (intentionally or otherwise).
I am working on a "pedagogical" proof of Harsanyi's theorem, providing necessary and sufficient conditions for purification to apply to a specific equilibrium. I hope to show that purifiability is equivalent to an equilibrium being essential (ie. the correspondence from utilities to equilibria being lower hemicontinuous at the equilibrium). It suffices that an equilibrium is robust to a simple class of non-idiosyncratic utility perturbations.
With Guillaume Fréchette and Andrew Schotter
Does the future beyond one's lifespan "cast a shadow"?
Repeated game frameworks typically assume that players' incentives are tied to their agency: players choose an action in each round they receive a payoff from. In reality, however, incentives often outlive agency: politicians and diplomats have an interest in their nation's standing beyond their time in office; a corporate executive's stock compensation means that they have an interest in the continued success of their company beyond their tenure. While agents do not exert direct agency over these outcomes, they may indirectly influence these outcomes through their current interactions.
We experimentally test whether these future incentives affect current strategies with an intergenerational prisoner's dilemma game where subjects are incentivized to care about their descendent's performance.