John W.E. Cremin
Postdoctoral fellow
,
Aix-Marseille Université
, Faculté d'économie et de gestion (FEG)
- Status
- Postdoctoral fellow
- Research domain(s)
- Game theory and social networks
- Thesis
- 2024, Columbia University
- Download
- CV
- Address
AMU - AMSE
5-9 Boulevard Maurice Bourdet, CS 50498
13205 Marseille Cedex 1- Website
John W. E. Cremin
Abstract
An agent, Sleeping Beauty, in a game with self-locating uncertainty (i.e. one play of the game visits the same information set multiple times, as in the paradox of the absentminded driver) must select a behavioural strategy that is self-ratifying: a best-response to the belief that her other instances do likewise. When there are multiple such fixed points, the standard treatment of Aumann et al. (1997) assumes that all instances of the agent can simply coordinate. I drop this assumption (supposing that Sleeping Beauty 'lose her magic psychic powers' ), and study said agent iteratively reasoning her way to an equilibrium selection instead. Which strategy other instances select can be seen as ambiguous, so I model Beauty's choice via a response function that encodes her response to ambiguity, and a procedure that describes in what manner she iterates the application of this response function. I consider two response functions, 'Bayesian' and EU-maximin, and two procedures, replacement and accumulation, and characterise in which cases the iterative reasoning converges. For either response function, accumulation always converges, but replacement does so if and only if there are no cycles of length weakly greater than two on a particular finite functional digraph I call the support digraph.
Keywords
Sleeping Beauty Problem, Imperfect Recall, Self-Locating Uncertainty, Decision Instability, Ambiguity, Absent-Minded Driver
John W. E. Cremin
Abstract
I study games with self-locating uncertainty in which an agent at a single information set is uncertain of his position evenwithina given information set of a given play of the game. In such games, there is an analogy to be drawn with Newcomb’s problem: in bothsettings, locally rational (thirder) reasoning and globally optimal (planning) reasoning can prescribe different strategies. I call this aNewcomb tension, and present a representation theorem: a Bayesian with commitment power and an uncommitted agent holding incorrect ‘one-boxer’ beliefs are behaviourally equivalent. In the single-agent case, randomisation always resolves the tension but in multi-agent games, in which planning and interim social weights diverge under some conditions, a multi-agent Newcomb tension can survive this randomisation resolution with an asymmetric awakening structure across agents. I consider the implications of this for the duplicating Sleeping Beauty problem, and a duplicating variant of the absent-minded driver.
Keywords
Sleeping Beauty Problem, Newcomb’s Problem, Self-Locating/Indexical Uncertainty, Imperfect Recall, Absent-Minded Driver
John W. E. Cremin
Abstract
I study games with self-locating uncertainty in which an agent at a single information set is uncertain of his position evenwithina given information set of a given play of the game. In such games, there is an analogy to be drawn with Newcomb’s problem: in bothsettings, locally rational (thirder) reasoning and globally optimal (planning) reasoning can prescribe different strategies. I call this aNewcomb tension, and present a representation theorem: a Bayesian with commitment power and an uncommitted agent holding incorrect ‘one-boxer’ beliefs are behaviourally equivalent. In the single-agent case, randomisation always resolves the tension but in multi-agent games, in which planning and interim social weights diverge under some conditions, a multi-agent Newcomb tension can survive this randomisation resolution with an asymmetric awakening structure across agents. I consider the implications of this for the duplicating Sleeping Beauty problem, and a duplicating variant of the absent-minded driver.
Keywords
Sleeping Beauty Problem, Newcomb’s Problem, Self-Locating/Indexical Uncertainty, Imperfect Recall, Absent-Minded Driver
John W. E. Cremin
Abstract
Models of social learning conventionally assume that all actions are visible, whereas in reality, we can often choose whether or not to advertise our choices. Inthis paper, I study a model of sequential social learning in which social agents choose whether or not to let successors see their action, only wanting to do so if they are sufficiently confident in their choice (they are timid), and noise agents act randomly. I find that in sparse networks, this produces a form of unravelling to the effect that noise agents are overrepresented. This can damage learning to an arbitrary extent if social agents are sufficiently timid. In dense networks, however, no such unravelling occurs, and the combination of noise and timidity can facilitate complete learning even with bounded beliefs.
Keywords
Sequential Social Learning, Endogenous Social Networks, Network Theory, Information Economics
John W. E. Cremin
Abstract
Models of social learning conventionally assume that all actions are visible, whereas in reality, we can often choose whether or not to advertise our choices. Inthis paper, I study a model of sequential social learning in which social agents choose whether or not to let successors see their action, only wanting to do so if they are sufficiently confident in their choice (they are timid), and noise agents act randomly. I find that in sparse networks, this produces a form of unravelling to the effect that noise agents are overrepresented. This can damage learning to an arbitrary extent if social agents are sufficiently timid. In dense networks, however, no such unravelling occurs, and the combination of noise and timidity can facilitate complete learning even with bounded beliefs.
Keywords
Sequential Social Learning, Endogenous Social Networks, Network Theory, Information Economics
John W. E. Cremin
Abstract
Modern society is increasingly polarized, even on purely factual questions, despite greater access to information than ever. In a model of sequential sociallearning, I study the impact ofmotivated reasoningon information aggregation. This is a belief formation process in which agents trade-off accuracy against ideological convenience. I find that even Bayesian agents only learn in very highly connected networks, where agents have arbitrarily large neighborhoods asymptotically. This is driven by the fact that motivated agents sometimes reject information that can be inferred from their neighbors’ actions when it refutes their desired beliefs. Observing any finite neighborhood, there is always some probability that all of an agent’s neighbors will have disregarded information thus. Moreover, I establish thatconsensus, where all agents eventually choose the same action, is only possible with relatively uninformative private signals and low levels of motivated reasoning.
Keywords
Social Learning, Motivated Reasoning, Networks, Polarization
John W. E. Cremin
Abstract
Modern society is increasingly polarized, even on purely factual questions, despite greater access to information than ever. In a model of sequential sociallearning, I study the impact ofmotivated reasoningon information aggregation. This is a belief formation process in which agents trade-off accuracy against ideological convenience. I find that even Bayesian agents only learn in very highly connected networks, where agents have arbitrarily large neighborhoods asymptotically. This is driven by the fact that motivated agents sometimes reject information that can be inferred from their neighbors’ actions when it refutes their desired beliefs. Observing any finite neighborhood, there is always some probability that all of an agent’s neighbors will have disregarded information thus. Moreover, I establish thatconsensus, where all agents eventually choose the same action, is only possible with relatively uninformative private signals and low levels of motivated reasoning.
Keywords
Social Learning, Motivated Reasoning, Networks, Polarization