Roger Hartley

Aggregative Public Good Games

We exploit the aggregative structure of the public good model to provide a simple analysis of the voluntary contribution game. In contrast to the best response function approach, ours avoids the proliferation of dimensions as the number of players is increased, and can readily analyze games involving many heterogeneous players. We demonstrate the approach at work on the standard pure public good model and show how it can analyze extensions of the basic model.

Can Expected Utility Theory Explain Gambling

We investigate the ability of expected utility theory to account for simultaneous gambling and insurance. Contrary to a previous claim that borrowing and lending in perfect capital markets rules out a demand for gambles, we show that expected utility theory with non-concave utility functions can still explain gambling. When the rates of interest and time preference are equal, agents will seek to gamble unless income falls in a finite set of exceptional values. When these rates differ, there will be a range of incomes for which gambles are desired. In both cases repeated gambling is not explained but market imperfections such as different borrowing and lending rates can account for persistent gambling provided the rates span the rate of time preference.

The Demand for Lotto: The Role of Conscious Selection

This article presents estimates of the elasticity of demand for lottery tickets using time series data in which there is variation in the expected value of a lottery ticket induced by rollovers. An important feature of our data is that there are far more rollovers than expected given the lottery design. We find strong evidence that individuals do not choose their lottery numbers uniformly from a uniform distribution—that is, conscious selection. We use our estimates to derive the inverse supply function for the industry, and this enables us to identify the demand elasticity. We find the price elasticity to be close to unity, which implies that the operator is revenue maximizing—which is the regulators objective.

Equilibrium Existence and Uniqueness in Public Good Models: An Elementary Proof via Contraction

This paper presents a proof for existence and uniqueness of a Nash equilibrium of a public good model that exploits a simple contraction mapping. The proof establishes both existence and uniqueness in a single exercise that provides intuition about sufficiency. The method of proof is applied not only to the basic pure public good model but also to the impure model. In the latter model, income normality does not play the same pivotal role for existence and uniqueness. Copyright 1999 by Blackwell Publishing Inc.(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)

Who really wants to be a millionaire? : estimates of risk aversion from gameshow data

This paper analyses the behaviour of contestants in one of the most popular TV gameshows ever to estimate risk aversion. This gameshow has a number of features that makes it well suited for our analysis: the format is extremely straightforward, it involves no strategic decision-making, we have a large number of observations, and the prizes are cash and paid immediately, and cover a large range – from £100 up to £1 million. Our data sources have the virtue that we are able to check the representativeness of the gameshow participants. Even though the CRRA model is extremely restrictive we find that a coefficient or relative risk aversion which is close to unity fits the data across a wide range of wealth remarkably well.

Vector Optimal Routing by Dynamic Programming

Algorithms for generating shortest paths have been widely studied in the combinational optimisation literature for many years. More recently, the vector version, in which non-dominated paths are sought, has been investigated. Acyclic problems were discussed by Randolph and Ringeisen1 and Thuente.2 The bicriterion case was analysed by Hansen3 and extended by Climaco and Martins4 and Martins.5 A multicriterion algorithm was given by Martins.6 White7 used linear programming methodology but was forced to exclude non-dominated paths which were dominated by a convex combination of path lengths.

Linear Multiple Objective Programming

Multiple objective optimisation has undergone considerable development in recent years and several approaches have been investigated. One of the closest to single objective optimisation is vector optimisation, in which efficient (non-dominated, admissible, Pareto optimal) solutions are sought. Since linear programming exhibits a particularly complete body of theory, we might expect the same to be true of vector linear programming and in this lecture we will describe some aspects of this theory.

On the design of lottery games

We describe a model of participation in lottery games designed to address the optimisation of tax revenue in state-sponsored lotteries. The model treats participants dynamically and examines a long-run equilibrium. A novel high frequency approximation is used to turn the problem into a static, state-contingent deterministic programming problem. We demonstrate that the solution of this problem has qualitatively plausible properties and then calibrate the model against the United Kingdom National Lottery (UKNL). The results suggest that the current design of the UKNL may not be maximising tax revenue.

ON ‘NICE’ AND ‘VERY NICE’ AUTARKIC EQUILIBRIA IN STRATEGIC MARKET GAMES*

We study a strategic market game in which traders are endowed with both a good and money and can choose whether to buy or sell the good. We derive conditions under which a non‐autarkic equilibrium exists and when the only equilibrium is autarky. Autarky is ‘nice’ (robust to small perturbations in the game) when it is the only equilibrium, and ‘very nice’ (robust to large perturbations) when no gains from trade exist. We characterize economies where autarky is nice but not very nice, i.e. when gains from trade exist and yet no trade takes place.

An existence and uniqueness theorem for an optimal inventory problem with forecasting

Abstract An existence and uniqueness theorem is proved for an optimal inventory problem with forecasting. The model assumes costs are fixed and that unsatisfied demand is lost. At each stage a forecast is obtained on the basis of which the decisionmaker has a known conditional probability distribution of demand. The theorem is a generalization of a result stated but not proved by White.