Willemien Kets

Random intersection graphs with tunable degree distribution and clustering

A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this article a model is developed in which each vertex is given a random weight and vertices with larger weights are more likely to be assigned large subsets. The distribution of the degree of a given vertex is characterized and is shown to depend on the weight of the vertex. In particular, if the weight distribution is a power law, the degree distribution will be as well. Furthermore, an asymptotic expression for the clustering in the graph is derived. By tuning the parameters of the model, it is possible to generate a graph with arbitrary clustering, expected degree, and—in the power-law case—tail exponent.

Inequality and Network Structure

This paper explores the manner in which the structure of a social network constrains the level of inequality that can be sustained among its members. We assume that any distribution of value across the network must be stable with respect to coalitional deviations, and that players can form a deviating coalition only if they constitute a clique in the network. We show that if the network is bipartite, there is a unique stable payoff distribution that is maximally unequal in that it does not Lorenz dominate any other stable distribution. We obtain a complete ordering of the class of bipartite networks and show that those with larger maximum independent sets can sustain greater levels of inequality. The intuition behind this result is that networks with larger maximum independent sets are more sparse and hence offer fewer opportunities for coalitional deviations. We also demonstrate that standard centrality measures do not consistently predict inequality. We extend our framework by allowing a group of players to deviate if they are all within distance k of each other, and show that the ranking of networks by the extent of extremal inequality is not invariant in k.

Congestion, Equilibrium and Learning: The Minority Game

The minority game is a simple congestion game in which the players’ main goal is to choose among two options the one that is adopted by the smallest number of players. We characterize the set of Nash equilibria and the limiting behavior of several well-known learning processes in the minority game with an arbitrary odd number of players. Interestingly, different learning processes provide considerably different predictions.

Learning to be Prepared

Behavioral economics provides several motivations for the common observation that agents appear somewhat unwilling to deviate from recent choices. More recent choices can be more salient than other choices, or more readily available in the agent’s mind. Alternatively, agents may have formed habits, or use rules of thumb. This paper provides discrete-time adjustment processes for strategic games in which players display such a bias towards recent choices. In addition, players choose best replies to beliefs supported by observed play in the recent past. We characterize the limit behavior of these processes by showing that they eventually settle down in minimal prep sets (Voorneveld in Games Econ Behav 48:403–414, 2004).

The Minority Game: An Economics Perspective

This paper gives a critical account of the minority game literature. The minority game is a simple congestion game: players need to choose between two options, and those who have selected the option chosen by the minority win. The learning model proposed in this literature seems to differ markedly from the learning models commonly used in economics. We relate the learning model from the minority game literature to standard game-theoretic learning models, and show that in fact it shares many features with these models. However, the predictions of the learning model differ considerably from the predictions of most other learning models. We discuss the main predictions of the learning model proposed in the minority game literature, and compare these to experimental findings on congestion games.

An Axiomatization of Minimal Curb Sets

Norde et al.[Games Econ.Behav. 12 (1996) 219] proved that none of the equilibrium concepts in the literature on equilibrium selection in finite strategic games satisfying existence is consistent.A transition to set-valued solution concepts overcomes the inconsistency problem: there is a multiplicity of consistent set-valued solution concepts that satisfy nonemptiness and recommend utility maximization in one-player games.The minimal curb sets of Basu and Weibull [Econ.Letters 36 (1991) 141] constitute one such solution concept; this solution concept is axiomatized in this article.

Learning with Fixed Rules: The Minority Game

This paper gives a critical account of the literature on adaptive behaviour in the minority game, a simple congestion game. The literature has proposed a model which differs markedly from many standard learning models in that players are endowed with a fixed subset of behavioural rules or response modes which map the observed history to actions. These rules need not have a behavioural interpretation or be derived from some form of optimizing behaviour. Nonetheless, this model gives rise to behaviour that is close to equilibrium behaviour at the aggregate level. The individual‐level behaviour predicted by the model seems to capture some aspects of observed experimental behaviour that are difficult to explain using standard models.

A Belief-Based Theory of Homophily

We introduce a model of homophily that does not rely on the assumption of homophilous preferences. Rather, it builds on the dual process account of Theory of Mind in psychology which focuses on the role of introspection in decision making. Homophily emerges because players find it easier to put themselves into the shoes of a member of their own group. Endogenizing the drivers of homophily permits us to derive novel comparative statics results and to explain commonly observed features of social and economic networks.

Challenging Conformity: A Case for Diversity

Why do diverse groups outperform homogeneous groups in some settings, but not in others? We show that while diverse groups experience more frictions than homogeneous ones, they are also less conformist. Homogeneous groups minimize the risk of miscoordination, but they may get stuck in an inefficient equilibrium. Diverse groups may fail to coordinate, but if they do, they tend to attain efficiency. This fundamental tradeoff determines how the optimal level of diversity varies with social and economic factors. When it is vitally important to avoid miscoordination, homogeneous groups are optimal. However, when it is critical to implement new and efficient practices, diverse groups perform better.

Betting strategies, market selection, and the wisdom of crowds

We investigate the limiting behavior of trader wealth and prices in a simple prediction market with a finite set of participants having heterogeneous beliefs. Traders bet repeatedly on the outcome of a binary event with fixed Bernoulli success probability. A class of strategies, including (fractional) Kelly betting and constant relative risk aversion (CRRA) are considered. We show that when traders are willing to risk only a small fraction of their wealth in any period, belief heterogeneity can persist indefinitely; if bets are large in proportion to wealth then only the most accurate belief type survives. The market price is more accurate in the long run when traders with less accurate beliefs also survive. That is, the survival of traders with heterogeneous beliefs, some less accurate than others, allows the market price to better reflect the objective probability of the event in the long run.