On payoff heterogeneity in games with strategic complementarities

Payoff heterogeneity weakens positive feedback in binary choice models in two ways. First, heterogeneity drives individuals to corners where they are unaffected by strategic complementarities. Second, aggregate behaviour is smoother than individual behaviour when individuals are heterogeneous. However, this smoothing does not necessarily eliminate positive feedback or guarantee a unique equilibrium. In games with an unbounded, continuous choice space, heterogeneity may either weaken or strengthen positive feedback, depending on a simple convexity/concavity condition. We conclude that positive feedback phenomena derived in representative agent models will often be robust to heterogeneity.Heterogeneity, multiplicity, discrete choice, strategic complementarity, positive feedback

Ratification quotas in international agreements

This paper analyses the role of ratification quotas in multilateral agreements over emission reduction. The higher is the quota, the lower is the level of emissions in case the agreement comes into force, but the higher is also the risk of failure. In a setting with incomplete information, two country types and a binary contribution to the provision, I examine the differences between simultaneous and sequential ratification. When the benefits from emission of both types are smaller than the social costs, the outcome in the simultaneous case is essentially identical to the sequential case. The optimal quota is 100% and achieves the first best. With the high type's benefits exceeding the social costs, I find that the optimal quota is as small as possible, if ratification is simultaneous. In the sequential ratification case, I cannot determine the optimal quota. However, I find that the aggregate expected surplus decreases with respect to the simultaneous case

Inclusive Cognitive Hierarchy

Cognitive hierarchy theory, a collection of structural models of non-equilibrium thinking, in which players' best responses rely on heterogeneous beliefs on others' strategies including naive behavior, proved powerful in explaining observations from a wide range of games. We introduce an inclusive cognitive hierarchy model, in which players do not rule out the possibility of facing opponents at their own thinking level. Our theoretical results show that inclusiveness is crucial for asymptotic properties of deviations from equilibrium behavior in expansive games. We show that the limiting behaviors are categorized in three distinct types: naive, Savage rational with inconsistent beliefs, and sophisticated. We test the model in a laboratory experiment of collective decision-making. The data suggests that inclusiveness is indispensable with regard to explanatory power of the models of hierarchical thinking.Series: Department of Strategy and Innovation Working Paper Serie

Quantum Probabilities as Behavioral Probabilities

We demonstrate that behavioral probabilities of human decision makers share many common features with quantum probabilities. This does not imply that humans are some quantum objects, but just shows that the mathematics of quantum theory is applicable to the description of human decision making. The applicability of quantum rules for describing decision making is connected with the nontrivial process of making decisions in the case of composite prospects under uncertainty. Such a process involves deliberations of a decision maker when making a choice. In addition to the evaluation of the utilities of considered prospects, real decision makers also appreciate their respective attractiveness. Therefore, human choice is not based solely on the utility of prospects, but includes the necessity of resolving the utility-attraction duality. In order to justify that human consciousness really functions similarly to the rules of quantum theory, we develop an approach defining human behavioral probabilities as the probabilities determined by quantum rules. We show that quantum behavioral probabilities of humans not merely explain qualitatively how human decisions are made, but they predict quantitative values of the behavioral probabilities. Analyzing a large set of empirical data, we find good quantitative agreement between theoretical predictions and observed experimental data.Comment: Latex file, 32 page

Risk and Wealth in a Model of Self-fulfilling Currency Crises

Market participants' risk attitudes, wealth and portfolio composition influence their positions in a pegged foreign currency and, therefore, may have important effects on the sustainability of currency pegs. We analyze such effects in a global game model of currency crises with continuous action choices. The model, solved in closed form, generates a rich set of theoretical predictions consistent with many popular and academic (unmodelled) speculations about the onset and timing of currency crises. The results extend linearly to a heterogeneous agent population.Currency crisis, Global games, Risk aversion, Wealth, Portfolio

Endogenous equilibria in liquid markets with frictions and boundedly rational agents

In this paper we propose a simple binary mean field game, where N agents may decide whether to trade or not a share of a risky asset in a liquid market. The asset's returns are endogenously determined taking into account demand and transaction costs. Agents' utility depends on the aggregate demand, which is determined by all agents' observed and forecasted actions. Agents are boundedly rational in the sense that they can go wrong choosing their optimal strategy. The explicit dependence on past actions generates endogenous dynamics of the system. We, firstly, study under a rather general setting (risk attitudes, pricing rules and noises) the aggregate demand for the asset, the emerging returns and the structure of the equilibria of the asymptotic game. It is shown that multiple Nash equilibria may arise. Stability conditions are characterized, in particular boom and crash cycles are detected. Then we precisely analyze properties of equilibria under significant examples, performing comparative statics exercises and showing the stabilizing property of exogenous transaction costs.Endogenous dynamics; Nash equilibria; Bounded rationality; Transaction costs; Mean field games; Random utility

Who Matters in Coordination Problems?

We consider a common investment project that is vulnerable to a self-fulfilling coordination failure and hence is strategically risky. Based on their private information, agents { who have heterogeneous investment incentives - form expectations or "sentiments" about the project's outcome. We find that the sum of these sentiments is constant across different strategy profiles and it is independent of the distribution of incentives. As a result, we can think of sentiment as a scarce resource divided up among the different payoff types. Applying this finding, we show that agents who benefit little from the project's success have a large impact on the coordination process. The agents with small benefits invest only if their sentiment towards the project is large per unit investment cost. As the average sentiment is constant, a subsidy decreasing the investment costs of these agents will "free up" a large amount of sentiment, provoking a large impact on the whole economy. Intuitively, these agents, insensitive to the project's outcome and hence to the actions of others, are influential because they modify their equilibrium behavior only if the others change theirs substantially.Heterogeneous Agents, Global Games, Poverty Traps, Strategic Complementarity, Representative Agent.

Minimum Participation Rules with Heterogeneous Countries

Almost all international environmental agreements include a minimum participation rule. Under such a rule an agreement becomes legally binding if and only if a certain threshold in terms of membership or contribution is reached. We analyze a cartel game with open membership and heterogeneous countries to study the endogenous choice of a minimum participation rule and its role for the success of international environmental agreement

The UN in the lab

We consider two alternatives to inaction for governments combating terrorism, which we term Defense and Prevention. Defense consists of investing in resources that reduce the impact of an attack, and generates a negative externality to other governments, making their countries a more attractive objective for terrorists. In contrast, Prevention, which consists of investing in resources that reduce the ability of the terrorist organization to mount an attack, creates a positive externality by reducing the overall threat of terrorism for all. This interaction is captured using a simple 3×3 “Nested Prisoner’s Dilemma” game, with a single Nash equilibrium where both countries choose Defense. Due to the structure of this interaction, countries can benefit from coordination of policy choices, and international institutions (such as the UN) can be utilized to facilitate coordination by implementing agreements to share the burden of Prevention. We introduce an institution that implements a burden-sharing policy for Prevention, and investigate experimentally whether subjects coordinate on a cooperative strategy more frequently under different levels of cost sharing. In all treatments, burden sharing leaves the Prisoner’s Dilemma structure and Nash equilibrium of the game unchanged. We compare three levels of burden sharing to a baseline in a between-subjects design, and find that burden sharing generates a non-linear effect on the choice of the efficient Prevention strategy and overall performance. Only an institution supporting a high level of mandatory burden sharing generates a significant improvement in the use of the Prevention strategy

Ratification quotas in international agreements

This paper analyses the role of ratification quotas in multilateral agreements over emission reduction. The higher is the quota, the lower is the level of emissions in case the agreement comes into force, but the higher is also the risk of failure. In a setting with incomplete information, two country types and a binary contribution to the provision, I examine the differences between simultaneous and sequential ratification. When the benefits from emission of both types are smaller than the social costs, the outcome in the simultaneous case is essentially identical to the sequential case. The optimal quota is 100% and achieves the first best. With the high type's benefits exceeding the social costs, I find that the optimal quota is as small as possible, if ratification is simultaneous. In the sequential ratification case, I cannot determine the optimal quota. However, I find that the aggregate expected surplus decreases with respect to the simultaneous case.public goods; international bargaining; ratfication; emission games