Refereed publications
"Axioms for measuring utility on partial mixture sets," Journal of Mathematical Economics (2018)
Published version
This paper extends Herstein and Milnor's famous representation of preferences on a mixture set to settings where some pairs of prospects are not connected via a path of mixtures. This is useful when we wish to model a decision maker using cardinal, nonlinear utility. Eg when beliefs are ambiguous, paths between prospects that are not comonotonic are excluded.
Published version
This paper extends Herstein and Milnor's famous representation of preferences on a mixture set to settings where some pairs of prospects are not connected via a path of mixtures. This is useful when we wish to model a decision maker using cardinal, nonlinear utility. Eg when beliefs are ambiguous, paths between prospects that are not comonotonic are excluded.
"Axioms for parametric continuity when the topology is coarse," Journal of Mathematical Economics (2017), vol. 72, p. 88-94
Published version
Published version
"Sub-models for interactive unawareness," with S. Grant, J. J. Kline and J. Quiggin. Theory and Decision (2015), p. 1-13
Published version
Published version
Papers under review
Current working papers
"Prudent Inductive Inference"
Preprint
We consider a predictor that ranks eventualities according to their plausibility, given her current sample of past observations. Our contribution is to accommodate predictors that lack experience in the following sense: resampling past cases fails to generate a sufficiently diverse set of rankings. To do so, we weaken Gilboa and Schmeidler's (2003) 4-diversity axiom: for every subset of 4 eventualities, each of the 4 ! = 24 total rankings arise for some sample of past observations. Our corresponding condition, conditional 2-diversity is weaker than 3-diversity. We derive a nonparametric cardinal representation by instead assuming prudence: i.e. the predictor's model extends to higher dimensions (novel observations) without giving rise to behaviour that is intransitive, dogmatic (exclusion of new rankings) or revisionary (of current rankings). We relate our representation to (i) robust, nonparametric no-arbitrage conditions in bond markets; (ii) psychological evidence of intransitivity in novel situations; (iii) zero-day attacks.
Preprint
We consider a predictor that ranks eventualities according to their plausibility, given her current sample of past observations. Our contribution is to accommodate predictors that lack experience in the following sense: resampling past cases fails to generate a sufficiently diverse set of rankings. To do so, we weaken Gilboa and Schmeidler's (2003) 4-diversity axiom: for every subset of 4 eventualities, each of the 4 ! = 24 total rankings arise for some sample of past observations. Our corresponding condition, conditional 2-diversity is weaker than 3-diversity. We derive a nonparametric cardinal representation by instead assuming prudence: i.e. the predictor's model extends to higher dimensions (novel observations) without giving rise to behaviour that is intransitive, dogmatic (exclusion of new rankings) or revisionary (of current rankings). We relate our representation to (i) robust, nonparametric no-arbitrage conditions in bond markets; (ii) psychological evidence of intransitivity in novel situations; (iii) zero-day attacks.
"Optimal taxation in networks with informal production"
PDF file
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).
PDF file
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"
PDF file
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.
PDF file
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"
PDF file
PDF file
"From rough sets to crisp partitions: learning in sequential games with large state spaces," written in collaboration with J. Quiggin.
PDF file
PDF file
"Unawareness and partially observable expected utility maximisation in the context of a game"
PDF file
PDF file
