Abstract: This talk will introduce stochastic theories of choice.  Such theories are ubiquitous in mathematical psychology and were also intensively studied by economists in the 1950s-1970s.  Since then, they have persisted within economics mainly in the guise of discrete choice models in econometrics (such as logit and probit).  However, in recent years there has been a resurgence in interest in stochastic choice models amongst economic theorists.  This talk is intended as a simple introduction to the field and, if there is interest, a starting point for a mini-series of talks on classical models and recent developments.  The talk(s) will also present a few open questions and hopefully stimulate some research ideas.  The field embraces a lot of empirical work on the econometrics of choice.  While I’m not an econometrician, I will try to point to developments in that area, and certainly to interesting empirical questions, so hopefully the topic may also be of interest to the econometrically inclined.  There are now quite a few publicly available datasets with which to explore various empirical questions.  And of course…there will be donuts.

Abstract: This is “Lecture 2 of n” in the mini-series on stochastic choice.  The logit model is perhaps the most familiar model of stochastic choice to economists.  Last time I introduced the Luce model – which is essentially equivalent to logit – and showed that it is characterised by the Choice Axiom.  This talk will describe some other classical theoretical results on the logit model, including their proofs (which are elementary): two alternative characterisations, and the result that every logit model is also an independent random utility model.  The latter theorem is important for econometric applications.  Then I’ll describe some striking new theoretical results on (generalisations of) the logit that have appeared in the last couple of years.  I’m still getting to grips with these so there should be plenty of scope for discussion and debate (and correction of the speaker’s errors!), and hopefully even some avenues for further research.

Abstract: Under incomplete information, voluntary contributors to a public good hold independent private valuations for the public goods and are uncertain about each other’s valuations. When released to the sequential move game, early contributors are likely to be cautious in free-riding on future contributors. This presentation will focus on the sufficient condition under which the sequential game generates strictly higher expected contribution than simultaneous move games. A Bayesian setting model is adopted where there is an arbitrary number of agents and a fairly general distribution of types. I will go over some details about this conventional model as well as other striking new theoretical results on the sequential move public goods provision problem. Hopefully, some detailed extensions of my future research will also be presented. Happy to hear your comments and suggestions.

Abstract: Decision markets are mechanisms to elicit and aggregate information to optimise decision-making. In the presentation, we will introduce a multi-agent system where a principal needs to decide between multiple alternative actions. Contextual information about the outcomes of the actions is distributed over multiple self-interested agents. The principal uses a decision market to reward these agents to reveal their information. We present simulations that demonstrate that with a proper reward, agents can learn to use their information to make accurate reports about the outcomes, and thereby learn to help the principal to make good decisions. To provide a proper reward, the principal needs to use a stochastic decision rule to select the action. However, this is not necessarily in the interest of the principal. We therefore also analyse strategies that are learned when the decision rule is deterministic and therefore the rewards are not proper. Finally, we discuss a mechanism that allows the principal to keep the decision-making process efficient and deterministic. Our simulations show that in this mechanism, the principal can provide proper incentives to elicit and aggregate all relevant information without using the realised outcome to determine the reward.

Abstract: This talk discusses joint work with Simona Fabrizi, Steffen Lippert and Addison Pan.  There is a small literature that tests binary voting behaviour in the laboratory – think of voting in a jury trial (but without discussion between jurors).  Most of these experiments use symmetric loss functions – both types of error (convicting the innocent and acquitting the guilty) receive the same penalty – even when the unanimity rule is used to determine the outcome (i.e., the defendant is acquitted unless all jurors vote guilty).  There is one extant study (Anderson et al., 2015) that employs a loss function with a higher penalty for convicting the innocent, and its results show by far the largest difference between the data and the theoretical prediction.  We have conducted two more voting experiments involving an asymmetric loss function.   This talk discusses our results, as well as those of Anderson et al. (2015), and assesses the prospects of reconciling the data with theory.

Abstract: The first-past-the-post (FPP) divides the country into districts. On the other hand, proportional representation (PR) rules treat the country as the only district. These are the two extremes in the world of parliament choosing rules. Each of them has its own logic based on the concept of representation with both having positive and negative features. We investigate this logic and describe several ways in which we may try to alleviate the negative features of FPP and PR without sacrificing the positive ones. This idea leads us to creating the hybrid voting systems, one of which is the mixed-member-proportional system (MMP) that New Zealand is using today. We look at the ways it can be further improved. We also look at the voting systems that can emerge in the future with the advances of computer technology, in particular, those based on the idea of creation not geographic but virtual districts - an old idea of Charles Dodgson that will soon become feasible within the limits of our computational capabilities. 

Abstract:  The Luce (a.k.a. Logit) model is a standard formalism for describing stochastic choice behaviour.  This paper explores its empirical signature: the properties of choice behaviour which are necessary and sufficient for representation by a Luce model.  This signature is well known in two special cases.  If choice is observed from all choice sets that can be constructed from a given (finite) universe of alternatives, then Luce’s (1959) IIA Axiom provides the required signature.  If choice is only observed from the binary menus then the Product Rule condition is necessary and sufficient. Both of these results are classical.  More recently, Echenique and Saito (2019) and, independently, Ahumada and Ülkü (2018) showed that a condition known as Cyclical Independence provides the required empirical signature when choice is observed from an arbitrary collection of choice sets.  We adapt results from the (closely related) literature on Harsanyi’s “common prior” problem to refine this characterisation of the Luce model.  Our results are useful for (i) designing efficient tests for Luce rationality; and (ii) constructing optimally informative choice sets for experiments, where it is usually only feasible to observe behaviour for a restricted number of choice situations.

Abstract:  Dr Addison Pan, in her new role as the International Networks Manager in the International Office at UoA, will give an overview of funding opportunities available to support research activities within research centres, such as the CMSS,  in the context of various initiatives the UoA is adhering to, partnering with other institutions overseas and diverse networks.

Abstract:  We investigate the question under which conditions asymmetric players with differing payoff parameters cooperate in an infinitely repeated discounted Prisoner’s Dilemma. Starting from established theory for the symmetric case we generalize to two distinct criteria which differ in their prediction about whether the willingness or ability of the two different players to cooperate are substitutes or complements. Finally, we run experiments designed to disentangle which of these two criteria predicts better.

Abstract:  Eyster et al. (2021) proposed a monopoly pricing theory with consumer fairness. In their paper, they assumed that consumers have fairness concerns and dislike unfair prices. Then, when a price rises due to a cost increase, consumers partially misattribute the higher price to higher markup—which they find unfair. A monopolist anticipates this response and adjusts their pricing strategies accordingly. I want to extend this work, by considering the duopoly (competitive) case, to understand how these effects might affect duopoly pricing under fairness concerns in an inflationary scenario, i.e., when consumers might find it increasingly more difficult to attribute price hikes to true underlying increasing costs, or to higher markups.

Abstract:  Fishburn's alternating scheme domains occupy a special place in the theory of Condorcet domains. Karpov (2023) generalised these domains and made an interesting observation proving that all of them are single-picked on a circle. However, an important point that all generalised Fishburn domains are maximal Condorcet domains remained unproved. We fill this gap and suggest a new combinatorial interpretation of generalised Fishburn's domains using black and white necklaces and white-convexity which provides a constructive proof of single-peakedness of these domains on a circle.  We show that classical single-peaked domains, single-dipped domains and Fishburn domains belong to the same family of domains while single-crossing domains do not as they are not even single-peaked on a circle.

Abstract:  I present a static model of what I call the Task Choice Game, for the 2-agent, 2-task case. In the Task Choice Game, individual agents decide how to allocate their (equal) working day over different tasks that must be collectively completed. Agents care about consumption, which is shared, and about their personal disutility of labour. I characterise envy-free equilibria for two types of preferences over tasks: specialisation (tasks as perfect substitutes) and variety (tasks as complements). I sketch a price mechanism which could deliver envy-free equilibrium allocations for large numbers of agents and tasks.