Competition analysis of a triopoly game with bounded rationality

A dynamic Cournot game characterized by three boundedly rational players is modeled by three nonlinear difference equations. The stability of the equilibria of the discrete dynamical system is analyzed. As some parameters of the model are varied, the stability of Nash equilibrium is lost and a complex chaotic behavior occurs. Numerical simulation results show that complex dynamics, such as, bifurcations and chaos are displayed when the value of speed of adjustment is high. The global complexity analysis can help players to take some measures and avoid the collapse of the output dynamic competition game.     

Study on a 3-dimensional game model with delayed bounded rationality

A nonlinear dynamic triopoly game model is studied based on the theory of nonlinear dynamics and previous researches in this paper. A lagged structure is introduced to the model to study stability conditions of the Nash equilibrium under a local adjustment process when players price their products with delayed bounded rationality. Numerical simulations are provided to demonstrate the complexity of system evolvement and influence of the strategy of delayed bounded rationality on system stability. We find that besides the lagged structure, suitable delayed parameters are also important factors to eliminate chaos or expand the stable region of the system, and various players’ adjustment parameters have different effect on stability of the system.     

On coordination of supply chain based on information asymmetry of effort level and fuzzy market environment

The agent’s private information contributes greatly to a person to make principal decision in the supply of a chain coordination. Therefore, it is a great issue for him to design an effective incentive mechanism in order to get the true information from the agent in his principle making. Assuming that the demand depend upon an agent’s effort level and the fuzzy market condition, the author in this paper researches and analyzes the principle-agent problem under fuzzy information asymmetry condition by using the theory of principal-agent as well as incentive mechanism.     

An information theoretic model of bounded rationality

Bounded rationality forces an entity to divide its responses between those it does immediately (called adaptedness) and those it does with delay (called adaptability). Information theory is used to show how coding is related to the problem of choosing between adaptedness and adaptability.     

Monotone and bounded interval equilibria in a coordination game with information aggregation

We analyze how private learning in a class of games with common stochastic payoffs affects the form of equilibria, and how properties such as player welfare and the extent of strategic miscoordination relate across monotone and non-monotone equilibria. Researchers typically focus on monotone equilibria. We provide conditions under which non-monotone equilibria also exist, where players attempt to coordinate to obtain the stochastic payoff whenever signals are in a bounded interval. In bounded interval equilibria (BIE), an endogenous fear of miscoordination discourages players from coordinating to obtain the stochastic payoff when their signals suggest coordination is most beneficial. In contrast to monotone equilibria, expected payoffs from successful coordination in BIE are lower than the ex-ante expected payoff from ignoring signals and always trying to coordinate to obtain the stochastic payoff. We show that BIE only exist when, absent private information, the game would be a coordination game.     

The dynamics of Bowley's model with bounded rationality

A nonlinear dynamical system which describe the time evolution of n-competitors in a Cournot game (Bowley's model) with bounded rationality is analyzed. The existence and stability of the equilibria of this system is studied. The stability conditions of the steady states for two and three players are explicitly computed. Complex behavior such as cycles and chaotic behavior are observed by numerical simulation. Delayed Bowley's with bounded rationality in monopoly is studied. We show that firms using bounded rationality with delay has a higher chance of reaching Nash equilibrium.     

The dynamics of Bertrand model with bounded rationality

The paper considers a Bertrand model with bounded rational. A duopoly game is modelled by two nonlinear difference equations. By using the theory of bifurcations of dynamical systems, the existence and stability for the equilibria of this system are obtained. Numerical simulations used to show bifurcations diagrams, phase portraits for various parameters and sensitive dependence on initial conditions. We observe that an increase of the speed of adjustment of bounded rational player may change the stability of Nash equilibrium point and cause bifurcation and chaos to occur. The analysis and results in this paper are interesting in mathematics and economics.     

The impacts of the full returns policy on a supply chain with information asymmetry

In contrast to the existing return policies literature assuming that information is symmetrical between the manufacturer and the retailer, we study the full returns policy’s impact on supply chains with information asymmetry. We first study the case that the base level of the demand follows a discrete distribution with two states. We find that the retailer benefits from the full returns policy in all circumstances, while the manufacturer and the supply chain are better off under some conditions. We then consider the situation in which the base level of the demand is a type of AR(1) process.     

Supply contracting and process innovation in a dynamic supply chain with information asymmetry

We investigate the process innovation and contracting decisions of a dynamic supply chain consisting of a supplier and a manufacturer, with the manufacturer possessing private information about her efficiency of process innovation. To overcome the potential adverse selection problem due to the asymmetric information, the supplier designs a menu of supply contracts that stipulates both the wholesale price and the purchasing quantity. We find that under information asymmetry, the supplier will optimally set a higher wholesale price but a lower purchasing quantity for the manufacturer with high innovation efficiency than that for the manufacturer with low innovation efficiency. As a consequence, the manufacturer with high innovation efficiency will significantly underinvest in innovation due to information asymmetry in addition to the impact of the double marginalization effect. Moreover, although a longer contract period tends to better motivate innovation, it can also magnify the influences of adverse selection on supply chain contracting, leading to a higher wholesale price for the manufacturer with high innovation efficiency.     

Pricing in a supply chain for auction bidding under information asymmetry

We examine a supply chain in which a manufacturer participates in a sealed-bid lowest price procurement auction through a distributor. This form of supply chain is common when a manufacturer is active in an overseas market without establishing a local subsidiary. To gain a strategic advantage in the division of profit, the manufacturer and distributor may intentionally conceal information about the underlying cost distribution of the competition. In this environment of information asymmetry, we determine the equilibrium mark-up, the ex-ante expected mark-up and expected profit of the manufacturer and the equilibrium bid of the distributor. In unilateral communication, we demonstrate the informed agent’s advantage resulting to higher mark-up. Under information sharing, we show that profit is equally shared among the supply chain partners and we explicitly derive the mark-up when the underlying cost distribution is uniform in [0, 1]. The model and findings are illustrated by a numerical example.     

Nonlinear dynamics in a heterogeneous duopoly game with adjusting players and diseconomies of scale

A repeated, discrete time, heterogeneous Cournot duopoly game with bounded rational and adaptive players adjusting the quantities of production is subject of investigation. Linear inverse demand function and quadratic cost functions reflecting decreasing returns to scale are assumed. The game is modeled with a system of two difference equations. Evolution of outputs over time is obtained by iteration of a two dimensional nonlinear map. Existing equilibria and their stability are analyzed. In face of diseconomies of scale, bounded rational and adaptive duopolists are shown to experience a decrease in the latitude of their output adjustment decisions with respect to the market stability compared to constant returns to scale and ceteris paribus. Chaotic dynamics is confirmed to depend mainly on the adjustment behavior of the bounded rational player, who if overshoots leaves the adaptive player with limited opportunities to stabilize the market again, hence industries facing diseconomies of scale are found to be less stable than those with constant marginal costs. Complexity of the dynamical system is examined by means of numerical simulations, where the paper extends the results of other authors who considered analogous games assuming linear cost functions. Intermittent transition to chaos and attractor merging crisis are shown among others.     

Complex dynamics and multistability with increasing rationality in market games

In this work we study oligopoly models in which firms adopt decision mechanisms based on best response techniques with different rationality degrees. Firms are also assumed to face resource or financial constraints in adjusting their production levels, so that, from time to time, they can only increase or decrease their strategy by a bounded quantity. We consider different families of oligopolies of generic sizes, characterized by heterogeneous compositions with respect to the rationality degrees of firms. We analytically study the local stability of the equilibrium depending on the oligopoly size and composition and through numerical simulations we investigate the possible dynamics arising when trajectories do not converge toward the equilibrium. We show that in this case complex dynamics can arise, and this is due to both the loss of stability of the equilibrium and to the emergence of multiple attractors, with the stable steady state coexisting with a different, periodic or chaotic, attractor. In particular, we show that multistability phenomena occur when the overall degree of rationality of the oligopoly is increased. Finally, we investigate the effect of non-convergent dynamics on the realized profits.     

Equilibria and dynamics of supply chain network competition with information asymmetry in quality and minimum quality standards

In this paper, we construct a supply chain network model with information asymmetry in product quality. The competing, profit-maximizing firms with, possibly, multiple manufacturing plants, which may be located on-shore or off-shore, are aware of the quality of the product that they produce but consumers, at the demand markets, only know the average quality. Such a framework is relevant to products ranging from certain foods to pharmaceuticals. We propose both an equilibrium model and its dynamic counterpart and demonstrate how minimum quality standards can be incorporated. Qualitative results as well as an algorithm are presented, along with convergence results. The numerical examples, accompanied by sensitivity analysis, reveal interesting results and insights for firms, consumers, as well as policy-makers, who impose the minimum quality standards.     

Fuzzy relations for the analysis of traders’ preferences in an information market game

In this paper we focus on preference and decision data gathered during a computer-supported information market game in which 35 students participated during seven consecutive trading sessions. The participants’ individual preferences on the market shares are collected to calculate a collective preference ranking using the Borda social choice method. Comparing this preference ranking to the shares’ actual market ranking resulting from the participants’ trading, we find a statistically significant difference between both rankings. As the preferences established by market behavior cannot be adequately explained through a social choice rule, we propose an alternative explanation based on the herd behavior phenomenon where traders imitate the most successful trader in the market. Using a decision analysis technique based on fuzzy relations, we study the participants’ rankings of the best share in the market during 7 weeks and compare the most successful trader to the other traders. The results from our analysis show that a substantial number of traders is indeed following the market leader.     

Notes on a stochastic game with information structure

International Journal of Game Theory -     

Local and global dynamics in a duopoly with price competition and market share delegation

This paper aims at studying a nonlinear dynamic duopoly model with price competition and horizontal product differentiation augmented with managerial firms, where managers behave according to market share delegation contracts. Ownership and management are then separate and managers are paid through adequate incentives in order to achieve a competitive advantage in the market. In this context, we show that complexity arises, related both to the structure of the attractors of the system and the structure of their basins, as multistability occurs. The study is conducted by combining analytical and numerical techniques, and aims at showing that slight different initial conditions may cause very different long-term outcomes.     

A smuggling game with asymmetrical information of players

This paper deals with a smuggling game with multiple stages. Customs is allowed to patrol within the limited number of chances and obtain reward by the capture of a smuggler. The smuggler gets a reward depending on the amount of contraband he succeeds to ship in smuggling at each stage. The pay-off of the game is zero-sum. In almost all past studies, they adopt the alternative of smuggling or non-smuggling as the smuggler's strategy. From the point of view of information, some researchers assumed that both players could observe their opponent's behaviour at the past stage or a few assumed that both players had no information about their opponent. Other than these types of smuggling games with the symmetric information, we introduce the asymmetrical acquisition of information or the concept of perfect Bayesian equilibrium in the smuggling game for the first time.     

Complex dynamics and chaos control of duopoly Bertrand model in Chinese air-conditioning market

A dynamic duopoly Bertrand model with quadratic cost function which is closer to reality and different from previous researches is discussed. The model is applied into air-conditioning market where the boundary equilibrium point is locally stable. Numerical simulations illustrate that the stability of Nash equilibrium strongly depends on the speed of adjustment of bounded rational player. The adjustment speeds and the degree of substitutability may undermine the stability of the equilibrium and cause a market structure to behave chaotically. The Lyapunov dimension of the chaos attractor is 1.9585 under some conditions. The stabilization of the chaotic behavior can be obtained by reducing the degree of substitutability. The results have an important theoretical and practical significance to Chinese air-conditioning market.     

Contracting with asymmetric demand information in supply chains

We solve a buyback contract design problem for a supplier who is working with a retailer who possesses private information about the demand distribution. We model the retailer’s private information as a space of either discrete or continuous demand states so that only the retailer knows its demand state and the demand for the product is stochastically increasing in the state. We focus on contracts that are viable in practice, where the buyback price being strictly less than the wholesale price, which is itself strictly less than the retail price. We derive the optimal (for the supplier) buyback contract that allows for arbitrary allocation of profits to the retailer (subject to the retailer’s reservation profit requirements) and show that in the limit this contract leads to the first-best solution with the supplier keeping the entire channel’s profit (after the retailer’s reservation profit).     

Hybrid pricing in a coupled European power market with more wind power

In the European electricity market, the promotion of wind power leads to more network congestion. Zonal pricing (market coupling), which does not take the physical characteristics of transmission into account, is the most commonly used method to relieve network congestion in Europe. However, zonal pricing fails to provide adequate locational price signals regarding scarcity of energy and thus creates a large amount of unscheduled cross-border flows originating from wind-generated power. In this paper, we investigate the effects of applying a hybrid congestion management model, i.e., a nodal pricing model for one country embedded in a zonal pricing system for the rest of the market. We find that, compared to full nodal pricing, hybrid pricing fails to fully utilize all the resources in the network and some wrong price signals might be given. However, hybrid pricing still outperforms zonal pricing. The results from the study cases show that, within the area applying nodal pricing, better price signals are given; the need for re-dispatching is reduced; more congestion rent is collected domestically and the unit cost of power is reduced.