Refereed publications
Axioms for measuring utility on partial mixture sets, Journal of Mathematical Economics Published version
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Axioms for parametric continuity when the topology is coarse, Journal of Mathematical Economics (2017), vol. 72, p. 88-94 Published version
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Sub-models for interactive unawareness, written in collaboration with S. Grant, J. J. Kline and J. Quiggin.
Theory and Decision (2015), p. 1-13 Published version
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Theory and Decision (2015), p. 1-13 Published version
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Papers under review
Current working papers
Prudent case-based prediction when experience is lacking
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Abstract:
Before 1697, it would be difficult for a European zoologist to justify the prediction ``the swans in New Holland are black''.
Yet the predictor might well be open-minded enough to formulate her current forecast so as to accommodate such a prediction if, and when, a new case (observed or theoretical) arrives. Moreover, she may be prudent enough to do so in such a way that, the current forecast has the potential to extend to novel cases without revision and without violation of basic rationality conditions.
In this article, we formalise these concepts and, to our knowledge, provide the first axiomatisation of the full set of additive and suitably unique similarity representations. The diverse matrix representation of Gilboa and Schmeidler (2003) is an important special case: the one where the predictor is experienced.
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Abstract:
Before 1697, it would be difficult for a European zoologist to justify the prediction ``the swans in New Holland are black''.
Yet the predictor might well be open-minded enough to formulate her current forecast so as to accommodate such a prediction if, and when, a new case (observed or theoretical) arrives. Moreover, she may be prudent enough to do so in such a way that, the current forecast has the potential to extend to novel cases without revision and without violation of basic rationality conditions.
In this article, we formalise these concepts and, to our knowledge, provide the first axiomatisation of the full set of additive and suitably unique similarity representations. The diverse matrix representation of Gilboa and Schmeidler (2003) is an important special case: the one where the predictor is experienced.
Optimal taxation in networks with informal production
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Abstract: Informal production is a key part of any developing economy. We extend Diamond--Mirrlees to a game-theoretic setting where informal firms (and consumers) are too-small-to-catch. That is, the government's cost of observing a transaction (and taxing it) is infinite if both parties to the transaction are small and zero otherwise. Thus, our starting point is that a transaction is only formal if at least one party is formal (faces initially increasing returns to scale). We assume a fixed production network (without cycles) of markets (with free entry) and postulate a zero-tax equilibrium. A withholding tax on formal inputs increases the local capacity for taxation. The constrained optimal policy is a correspondence on transaction bundles. The formation of conglomerates minimises price distortions and reconfigures the network. Production efficiency is restored if, and only if, (i) every supply chain contains a formal transaction and (ii) the level of development is enough to mitigate diseconomies of scope due to bundling across goods that are unrelated in production. The latter condition suggests a role for government investment in key sectors (such as infrastructure, IT and finance).
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Abstract: Informal production is a key part of any developing economy. We extend Diamond--Mirrlees to a game-theoretic setting where informal firms (and consumers) are too-small-to-catch. That is, the government's cost of observing a transaction (and taxing it) is infinite if both parties to the transaction are small and zero otherwise. Thus, our starting point is that a transaction is only formal if at least one party is formal (faces initially increasing returns to scale). We assume a fixed production network (without cycles) of markets (with free entry) and postulate a zero-tax equilibrium. A withholding tax on formal inputs increases the local capacity for taxation. The constrained optimal policy is a correspondence on transaction bundles. The formation of conglomerates minimises price distortions and reconfigures the network. Production efficiency is restored if, and only if, (i) every supply chain contains a formal transaction and (ii) the level of development is enough to mitigate diseconomies of scope due to bundling across goods that are unrelated in production. The latter condition suggests a role for government investment in key sectors (such as infrastructure, IT and finance).
Further projects
Eliciting beliefs about stock prices
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Abstract: Stock prices evolve in continuous time generating a state space that is infinite dimensional. In such spaces, even the simplest horse-lotteries (binary options) on the most basic events (cylinder sets) are unwieldy and difficult to evaluate. Yet events are the basic building blocks of the standard Bayesian model of Savage or Anscombe and Aumann. This supports the view (of Savage) that Bayesian beliefs are better suited to small worlds, where events are easy to describe. We propose an alternative foundation for eliciting subjective beliefs about the law of a given stock price from an agent. We consider the daily trajectory of a given stock price. Each trajectory is the image of a random path in the set of prospects. Together, these paths form a partial mixture set which we use to elicit subjective statistical moments about the stock prices. Using the generality of (partial) mixture sets we translate axioms on moments into standard axioms for a subjective expected utility representation. Since a full elicitation of beliefs is unfeasible when the state space is infinite-dimensional, we formalise a procedure for partially eliciting beliefs via a finite number of moments and propose a maximum entropy distribution to characterise beliefs.
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Abstract: Stock prices evolve in continuous time generating a state space that is infinite dimensional. In such spaces, even the simplest horse-lotteries (binary options) on the most basic events (cylinder sets) are unwieldy and difficult to evaluate. Yet events are the basic building blocks of the standard Bayesian model of Savage or Anscombe and Aumann. This supports the view (of Savage) that Bayesian beliefs are better suited to small worlds, where events are easy to describe. We propose an alternative foundation for eliciting subjective beliefs about the law of a given stock price from an agent. We consider the daily trajectory of a given stock price. Each trajectory is the image of a random path in the set of prospects. Together, these paths form a partial mixture set which we use to elicit subjective statistical moments about the stock prices. Using the generality of (partial) mixture sets we translate axioms on moments into standard axioms for a subjective expected utility representation. Since a full elicitation of beliefs is unfeasible when the state space is infinite-dimensional, we formalise a procedure for partially eliciting beliefs via a finite number of moments and propose a maximum entropy distribution to characterise beliefs.
Indecisive, belief-dependent preferences
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From rough sets to crisp partitions: learning in sequential games with large state spaces, written in collaboration with J. Quiggin.
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Unawareness and partially observable expected utility maximisation in the context of a game
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