Analysis of a duopoly game with heterogeneous players participating in carbon emission trading

In this paper, a price competition model with two heterogeneous players participating in carbon emission trading is formulated. The stable conditions of the equilibrium points of this system are discussed. Numerical simulations are used to show bifurcation diagrams, strange attractors, and sensitive dependence on initial conditions. We observe that the speed of adjustment of bounded rational player may change the stability of the Nash equilibrium and cause the system to behave chaotically. In addition, we find that the price of emission permits plays an important role in the duopoly game. The chaotic behavior of the system has been stabilized on the Nash equilibrium point by applying delay feedback control method

How do Zambian smallholder farmers allocate their budget? Evidence of dynamic decision-making based on a Cournot field experiment

Article accepted for the 35th International Conference of the System Dynamics Society, 16–20 July, 2017, Cambridge, MA, USA.Smallholder farmers in sub-Saharan Africa repeatedly face situations of complex and dynamic decision trade-offs, which include allocating money across short-term and long-term production activities. Short-term activities such as fertilizer application help to cover immediate food needs, but compromise future food production. Long- term production activities, such as building up soil fertility, are important systemic leverage points for future food production, but compromise present-day harvests. This article reports a Cournot field experiment conducted with Zambian farmers to investigate farm management decision-making in a dynamic context with conflicting production objectives. The results revealed that most Zambian smallholder farmers were biased towards short-term production activities, which led to suboptimal performance in production. Despite this bias, the farmers applied various distinct dynamic and non-dynamic decision strategies, with varying production outcomes. Simulation experiments with the decision strategies revealed that most decision strategies resulted in rather stable production patterns. However, following some decision strategies, the production patterns strongly varied when the strategies interacted with other strategies in the same market and the produce was therefore subject to the strategies’ endogenous interactions within the market. Given the farmers’ strong preference for fertilizer, the findings suggest that a shift towards favoring long-term oriented production activities is required to increase food production sustainably in sub-Saharan Africa. In conclusion, the various decision strategies and their endogenous interactions reinforce the need for building adaptive capacity among smallholder farmers in order to apply context-specific decision strategies.acceptedVersio

On the role of heuristics: Experimental evidence on inflation dynamics

We carry out an experiment on a macroeconomic price setting game where prices are complements. Despite relevant information being common knowledge and price flexibility we observe significant deviation from equilibrium prices and history dependence. In a first treatment we observe that equilibrium values were obtained in the long run but at the cost of a very slow adjustment and thus history dependence. By reporting a business indicator in a simpler form, subjects were given the chance to coordinate their prices by help of a heuristic in a second treatment. This option was widely taken, bringing about excess volatility and a deviation from equilibrium even in the long run. In a third treatment with staggered pricing we observe, contrary to theoretical predictions, the one-round ahead (publicly known) shock is significant, but future inflation is not. Our findings cast light on price dynamics when subjects have limited computational capacities. --Inflation Persistence,Staggered Prices,Sticky Reasoning,New Keynesian Phillips Curve

A Comprehensive Survey of Potential Game Approaches to Wireless Networks

Potential games form a class of non-cooperative games where unilateral improvement dynamics are guaranteed to converge in many practical cases. The potential game approach has been applied to a wide range of wireless network problems, particularly to a variety of channel assignment problems. In this paper, the properties of potential games are introduced, and games in wireless networks that have been proven to be potential games are comprehensively discussed.Comment: 44 pages, 6 figures, to appear in IEICE Transactions on Communications, vol. E98-B, no. 9, Sept. 201

The Spatial Agent-based Competition Model (SpAbCoM)

The paper presents a detailed documentation of the underlying concepts and methods of the Spatial Agent-based Competition Model (SpAbCoM). For instance, SpAbCoM is used to study firms' choices of spatial pricing policy (GRAUBNER et al., 2011a) or pricing and location under a framework of multi-firm spatial competition and two-dimensional markets (GRAUBNER et al., 2011b). While the simulation model is briefly introduced by means of relevant examples within the corresponding papers, the present paper serves two objectives. First, it presents a detailed discussion of the computational concepts that are used, particularly with respect to genetic algorithms (GAs). Second, it documents SpAbCoM and provides an overview of the structure of the simulation model and its dynamics. -- Das vorliegende Papier dokumentiert die zugrundeliegenden Konzepte und Methoden des Räumlichen Agenten-basierten Wettbewerbsmodells (Spatial Agent-based Competition Model) SpAbCoM. Anwendungsbeispiele dieses Simulationsmodells untersuchen die Entscheidung bezüglich der räumlichen Preisstrategie von Unternehmen (GRAUBNER et al., 2011a) oder Preissetzung und Standortwahl im Rahmen eines räumlichen Wettbewerbsmodells, welches mehr als einen Wettbewerber und zweidimensionalen Marktgebiete berücksichtigt. Während das Simulationsmodell in den jeweiligen Arbeiten kurz anhand eines Beispiels eingeführt wird, dient das vorliegende Papier zwei Zielen. Zum Einen sollen die verwendeten computergestützten Konzepte, hier speziell Genetische Algorithmen (GA), detailliert vorgestellt werden. Zum Anderen besteht die Absicht dieser Dokumentation darin, einen Überblick über die Struktur von SpAbCoM und die während einer Simulation ablaufenden Prozesse zu gegeben.Agent-based modelling,genetic algorithms,spatial pricing,location model.,Agent-basierte Modellierung,Genetische Algorithmen,räumliche Preissetzung,Standortmodell.

Essays on Games of Strategic Substitutes with Incomplete Information

This dissertation consists of three individual chapters. The first chapter applies lattice theoretic techniques in order to establish fundamental properties of Bayesian games of strategic substitutes (GSS) when the underlying type space is ordered either in increasing or decreasing first-order stochastic dominance. Existence and uniqueness of equilibria is considered, as well as the question of when such equilibria can be guaranteed to be monotone in type, a property which is used to guarantee monotone comparative statics. The second chapter uses the techniques of the first and combines them with the existing results for strategic complements (GSC) in order to extend the literature on global games under both GSC and GSS. In particular, the model of Carlsson and Van Damme (1993) is extended from 22 games to GSS or GSC involving a finite amount of players, each having a finite action space. Furthermore, the possibility that groups of players receive the same signal is allowed for, a condition which is new to the literature. It is shown that under this condition, the power of the model to resolve the issue of multiplicity is unambiguously increased. The third chapter considers stability of mixed strategy Nash equilibria in GSS. Chapter 1 analyzes Bayesian games of strategic substitutes under general conditions. In particular, when beliefs are order either increasingly or decreasingly by first order stochastic dominance, the existence and uniqueness, monotonicity, and comparative statics in this broad class of games are addressed. Unlike their supermodular counterpart, where the effect of an increase in type augments the strategic effect between own strategy and opponent’s strategy, submodularity produces competing effects when considering optimal responses. Using adaptive dynamics, conditions are given under which such games can be guaranteed to exhibit Bayesian Nash equilibria, and it is shown that in many applications these equilibria will be a profile of monotone strategies. Comparative statics of parametrized games is also analyzed using results from submodular games which are extended to incorporate incomplete information. Several examples are provided. The framework of Chapter 1 is applied to global games in Chapter 2. Global games methods are aimed at resolving issues of multiplicity of equilibria and coordination failure that arise in game theoretic models by relaxing common knowledge assumptions about an underlying parameter. These methods have recently received a lot of attention when the underlying complete information game is a GSC. Little has been done in this direction concerning GSS, however. This chapter complements the existing literature in both cases by extending the global games method developed by Carlsson and Van Damme (1993) to multiple player, multiple action GSS and GSC, using a p-dominance condition as the selection criterion. This approach helps circumvent recent criticisms to global games by relaxing some possibly unnatural assumptions on payoffs and parameters necessary to conduct analysis under current methods. The second part of this chapter generalizes the model by allowing groups of players to receive homogenous signals, which, under certain conditions, strengthens the model’s power of predictability. Chapter 3 analyzes the learning and stability of mixed strategy Nash equilibria in GSS, complementing recent work done in the case of GSC. Mixed strategies in GSS are of particular interest because it is well known that such games need not exhibit pure strategy Nash equilibria. First, a bound on the strategy space which indicate where randomizing behavior may occur in equilibrium is established. Second, it is shows that mixed strategy Nash equilibria are generally unstable under a wide variety of learning rules