Behavioral Game Theory

The final part of this exciting trilogy is cross-price elasticity. (See here for estimates of own price and income elasticity.) Here we are looking for how demand for one product, say cars, is influenced by the price of another product, say petrol. The idea is to find a spread of examples from goods that are close substitutes (have cross price elasticity near 1) to strong complements (have an elasticity near -1). Within the literature there are a lot more examples of substitutes, like cars and public transport, than of complements, like cars and petrol. Indeed, it was a bit of a struggle to find any complements. Here are the examples I converged on: The book versus culture number is taken from the study by Ringstad and Loyland. The numbers for organic food are taken from the report by Bunte and co-authors on Dutch data. Those for alcohol are from a UK a study by Meng and co-authors. For numbers of public transport in the UK there is a  study by Paulley and...

My previous blog looked at estimates of own price elasticity of demand. Now the focus moves on to estimates of income elasticity of demand. In a sense income elasticity should be easier to measure than price elasticity of demand because there is more variation in income than price. But I actually found it a lot harder to come by income elasticicities in the literature. And it was particularly difficult to get a nice spread of elasticities. Ideally we want some examples of luxury goods (with elasticity more than 1), normal goods (more than 0) and inferior goods (less than 0). The large majority of the examples I could find fitted in the 0.3-0.8 range. My rough interpretation of the literature is that 'simple' estimates tended to suggest things like eating out and health care were highly income elastic but more detailed work has lowered the numbers down. It was also the case that goods you might think of as luxuries where not. This could just be a self-selection issue. For i...

In the  textbook on Microeconomics and Behaviour with Bob Frank we have some tables giving examples of price, income and cross-price elasticities of demand. Given that most of the references are from the 70's I'm working on an update for the forthcoming 3rd edition. So, here is a brief overview of where the numbers come from for the table on price elasticity of demand. Suggestions for other good sources much appreciated. Before we get into the numbers - the disclaimer. Price elasticities are tricky things to tie down. Suppose you want the price elasticity of demand for cars. This elasticity is likely to be different for rich or poor people, people living in the city or the countryside, people in France or Germany etc.etc. You then have to think if you want the elasticity for buying a car or using a car (which includes petrol, insurance and so on). So, there is no such thing as the price elasticity of demand for cars. Moreover, the estimated price elasticity will depend o...

In the early days of its (modern) history game theory focused a lot on zero-sum games. These are games in which total payoffs always add to zero no matter what the outcome. So, in a two player setting - your gain is my loss and vice-versa. It was arguably natural for game theory to focus on zero-sum games because they represent the epitome of conflict. The main reason the focus fell on such games is, however, more one of convenience  - zero-sum games have a solution . This solution is captured by the minimax theorem and all that followed. Basically it amounts to saying that there is a unique way of playing a zero-sum game if all players want to maximize their payoff and are rational . Most games do not have a 'solution', because there are multiple Nash equilibria and so there is not an obvious correct way to play the game. In this sense zero-sum games are 'nice' or 'convenient'. But does it make sense to behave according to the minimax theorem? The simple an...

Recently I refereed a paper on the existence of Berge equilibrium. I must confess that until reading the paper I knew nothing of Berge equilibrium. But in my defence, the equilibrium does not get a mention in any game theory textbook on my shelves and, surely most telling of all, does not get an entry in Wikipedia. So, what is Berge equilibrium and should we hear more about it? The origins of the equilibrium are a book by French mathematician Claude Berge (who does get a Wikipedia page) on a general theory of n-person games, first published in 1957. But it has seemingly gone pretty much unnoticed from then on, although there is a growing literature on the topic as summarized in a 2017 paper by Larbani and Zhukovskii. The basic idea behind Berge equilibrium seems to be one of altruism or cooperation between players in a group. To explain, consider a game. Let s i denote the strategy of player i, s -i the strategies of everyone other than i and u i (s i , s -i ) the payoff of play...