Conjectural Equilibrium in Multiagent Learning

Learning in a multiagent environment is complicated by the fact that as other agents learn, the environment effectively changes. Moreover, other agents' actions are often not directly observable, and the actions taken by the learning agent can strongly bias which range of behaviors are encountered. We define the concept of a conjectural equilibrium, where all agents' expectations are realized, and each agent responds optimally to its expectations. We present a generic multiagent exchange situation, in which competitive behavior constitutes a conjectural equilibrium. We then introduce an agent that executes a more sophisticated strategic learning strategy, building a model of the response of other agents. We find that the system reliably converges to a conjectural equilibrium, but that the final result achieved is highly sensitive to initial belief. In essence, the strategic learner's actions tend to fulfill its expectations. Depending on the starting point, the agent may be better or worse off than had it not attempted to learn a model of the other agents at all.     

Computation of Multi-facility Location Nash Equilibria on a Network Under Quantity Competition

We deal with the location-quantity problem for competing firms when they locate multiple facilities and offer the same type of product. Competition is performed under delivered quantities that are sent from the facilities to the customers. This problem is reduced to a location game when the competing firms deliver the Cournot equilibrium quantities. While existence conditions for a Nash equilibrium of the location game have been discussed in many contributions in the literature, computing an equilibrium on a network when multiple facilities are to be located by each firm is a problem not previously addressed. We propose an integer linear programming formulation to fill this gap. The formulation solves the profit maximization problem for a firm, assuming that the other firms have fixed their facility locations. This allows us to compute location Nash equilibria by the best response procedure. A study with data of Spanish municipalities under different scenarios is presented and conclusions are drawn from a sensitivity analysis.

     

RFID-enabled item-level product information revelation

We consider a homogeneous product market and the incentive for oligopolists to share item-level product information with their customers. Enabled by Radio Frequency Identification technology, each firm has the option to record and reveal item-level information of a proportion of its products. We consider a two-stage game where each firm first decides its production plan and then determines its level of information revelation. With a constant clearance discount rate, we derive pure strategy equilibria that are subgame perfect and demonstrate that complete information sharing is the unique Nash equilibrium for the game when the common demand is volatile and that no information revelation is the unique Nash equilibrium when demand is not volatile. Furthermore, we show that the Nash equilibrium is the same with a decreasing clearance discount rate and that neither complete information revelation nor zero information revelation is consistent with an equilibrium with an increasing discount rate. Results are similar in a duopoly non-homogeneous product market scenario.     

The anatomy of foresight traps [foresight management]

No companies ever escape foresight traps. Foresight traps are inevitable because the ingredients for them are everywhere. Every trap has a technical or commercial surprise as part of the explanation. A new environment raises unfamiliar issues with established firms. Managing uncertainty often generates conflicts within a firm. Foresight traps can arise when managers let conflict interfere with their assessment of a competitive situation. An overconfident executive can make matters worse. Good firms do their best to save confident executives from their worst instincts. These firms collect information from a variety of sources, think hard about what their rivals perceive, and spend resources guarding against outcomes that might or might not arise.     

Bifurcation analysis of a dynamic duopoly model with heterogeneous costs and behavioural rules

We develop a nonlinear dynamic Cournot duopoly model in discrete time, where two bounded rational quantity-setting firms, both endowed with naïve expectations, are heterogeneous as to their cost functions and output strategies. One of the two competing firms adopts best-reply behaviour, whereas the other adjusts its production according to the gradient of its profit. Although excessive reaction of the latter firm generally results in destabilization of the ‘Cournot–Nash’ equilibrium and brings about complex dynamic scenarios, this occurs via qualitatively different bifurcation routes, depending on the ratio between firms’ marginal costs. The paper also provides a preliminary exploration of the long-run sustainability of the heterogeneous duopoly competition, by investigating numerically the impact of fixed costs on firms’ survival, along different output trajectories.     

Managing digital piracy under consumer valuation uncertainty: The roles of product demonstrations and antipiracy measures

Product demonstrations (e.g., software or video game trials) are commonly used in digital-good markets to resolve prospective consumers’ valuation uncertainty. We theoretically investigate how a monopolistic digital-good firm may utilize the tool of product demonstration, together with technical and legal antipiracy measures which increase the difficulty or cost of pirating, to optimally manage the impact of piracy on its new product’s profitability. We unexpectedly find that, in equilibrium, the firm’s profit may strictly decrease with the difficulty of pirating when the true product quality is not especially high, such that the firm chooses not to offer product demonstrations. This is because, with higher piracy costs, the firm has more incentive to offer product demonstrations and, as a result, rational customers’ quality belief conditional on non-demonstration is lower, which leads to a lower profit for the firm. We extend our model to incorporate consumers’ fit uncertainty about the product due to idiosyncratic tastes. Related managerial implications for public policy and legislation regarding piracy and copyright are discussed.     

Pharmaceutical supply chain networks with outsourcing under price and quality competition

In this paper, we present a pharmaceutical supply chain network model with outsourcing under price and quality competition, in both equilibrium and dynamic versions. We consider a pharmaceutical firm that is engaged in determining the optimal pharmaceutical flows associated with its supply chain network activities in the form of manufacturing and distribution. In addition to multimarket demand satisfaction, the pharmaceutical firm seeks to minimize its total cost, with the associated function also capturing the firm's weighted disrepute cost caused by possible quality issues associated with the contractors. Simultaneously, the contractors, who compete with one another noncooperatively in prices in the manner of Bertrand, and in quality, seek to secure manufacturing and distribution of the pharmaceutical product from the pharmaceutical firm. This game theory model allows for the determination of the optimal pharmaceutical product flows associated with the supply chain in‐house and outsourcing network activities and provides the pharmaceutical firm with its optimal make‐or‐buy decisions and the optimal contractor selections. We state the governing equilibrium conditions and derive the equivalent variational inequality formulation. We then propose dynamic adjustment processes for the evolution of the product flows, the quality levels, and the prices, along with stability analysis results. The algorithm yields a discretization of the continuous‐time adjustment processes. We present convergence results and compute solutions to numerical examples to illustrate the generality and applicability of the framework.     

Evaluation Metrics in Classification: A Quantification of Distance-Bias

This article provides a characterization of bias for evaluation metrics in classification (e.g., Information Gain, Gini, χ², etc.). Our characterization provides a uniform representation for all traditional evaluation metrics. Such representation leads naturally to a measure for the distance between the bias of two evaluation metrics. We give a practical value to our measure by observing the distance between the bias of two evaluation metrics and its correlation with differences in predictive accuracy when we compare two versions of the same learning algorithm that differ in the evaluation metric only. Experiments on real-world domains show how the expectations on accuracy differences generated by the distance-bias measure correlate with actual differences when the learning algorithm is simple (e.g., search for the best single feature or the best single rule). The correlation, however, weakens with more complex algorithms (e.g., learning decision trees). Our results show how interaction among learning components is a key factor to understand learning performance.     

Using Genetic Algorithms to Model the Evolution of Heterogeneous Beliefs

We study a general equilibrium system where agents have heterogeneous beliefs concerning realizations of possible outcomes. The actual outcomes feed back into beliefs thus creating a complicated nonlinear system. Beliefs are updated via a genetic algorithm learning process which we interpret as representing communication among agents in the economy. We are able to illustrate a simple principle: genetic algorithms can be implemented so that they represent pure learning effects (i.e., beliefs updating based on realizations of endogenous variables in an environment with heterogeneous beliefs). Agents optimally solve their maximization problem at each date given their beliefs at each date. We report the results of a set of computational experiments in which we find that our population of artificial adaptive agents is usually able to coordinate their beliefs so as to achieve the Pareto superior rational expectations equilibrium of the model.     

The Cournot game under a fuzzy decision environment

The conventional precision-based decision analysis methodology is invalid for business decision analysis when precise assessment data seldom exist. This paper considers the Cournot game with fuzzy demand and fuzzy costs that are assumed to be triangular fuzzy numbers. Our model utilizes the weighted center of gravity (WCoG) method to defuzzify the fuzzy profit function into a crisp value. We derive the equilibrium Cournot quantity of each firm by simultaneously solving the first-order condition of each firm. Our model explicitly derives the necessary condition to avoid an unreasonable outcome of negative equilibrium quantities and lack of flexibility for modification of the ranking method. In addition, we examine the standard deviation of the fuzzy profit resulting from the fuzziness of each firm’s cost and market demand functions. We conduct sensitivity analysis to investigate the effect of parameter perturbations on firms’ outcomes. The results indicate that the center of parameter plays an important role in sensitivity analysis and dominates over variations in equilibrium quantity due to a perturbation of fuzzy parameters.     

A Dynamic Model of Collective Bargaining

We use high-low search algorithms to compute equilibria in a multi-period model of collective bargaining. In this model, a group of workers bargains collectively with a firm which knows the per period incremental value v of each worker. The workers don't know their individual values, but use high-low search to learn them, given the known distribution of values in the group. In the first period the workers make a common wage demand w₁ and then the firm chooses a cutoff level y for the workers they will hire (i.e., those with v y). Since y is observable through numbers hired, workers may update their beliefs about their values, based on whether or not they were hired. In later periods workers with common beliefs make common wage demands. The main question addressed in the paper is how the firm can choose the hiring cutoff level to hinder the workers' learning process. We find (Theorem 1) that the firm's equilibrium strategy is to (i) hire some workers at a loss, and also (ii) to forego some profitable hirings. However (Theorem 2) the equilibrium outcome involves only the first kind of strategic loss by the firm. We also find (Theorem 3) that the firm's profit is less than when the worker optimizes against a predictable myopic firm (which chooses y=w₁). Thus the firm would wish to commit to the myopic hiring strategy if it were possible.     

Economic optimization using model predictive control with a terminal cost

In the standard model predictive control implementation, first a steady-state optimization yields the equilibrium point with minimal economic cost. Then, the deviation from the computed best steady state is chosen as the stage cost for the dynamic regulation problem. The computed best equilibrium point may not be the global minimum of the economic cost, and hence, choosing the economic cost as the stage cost for the dynamic regulation problem, rather than the deviation from the best steady state, offers potential for improving the economic performance of the system. It has been previously shown that the existing framework for MPC stability analysis, which addresses to the standard class of problems with a regulation objective, does not extend to economic MPC. Previous work on economic MPC developed new tools for stability analysis and identified sufficient conditions for asymptotic stability. These tools were developed for the terminal constraint MPC formulation, in which the system is stabilized by forcing the state to the best equilibrium point at the end of the horizon. In this work, we relax this constraint by imposing a region constraint on the terminal state instead of a point constraint, and adding a penalty on the terminal state to the regulator cost. We extend the stability analysis tools, developed for terminal constraint economic MPC, to the proposed formulation and establish that strict dissipativity is sufficient for guaranteeing asymptotic stability of the closed-loop system. We also show that the average closed-loop performance outperforms the best steady-state performance. For implementing the proposed formulation, a rigorous analysis for computing the appropriate terminal penalty and the terminal region is presented. A further extension, in which the terminal constraint is completely removed by modifying the regulator cost function, is also presented along with its stability analysis. Finally, an illustrative example is presented to demonstrate the differences between the terminal constraint and the proposed terminal penalty formulation.     

Cybersecurity investments with nonlinear budget constraints and conservation laws: variational equilibrium,marginal expected utilities,and Lagrange multipliers

In this paper, we propose a new cybersecurity investment supply chain game theory model, assuming that the demands for the product are known and fixed and, hence, the conservation law of each demand market is fulfilled. The model is a generalized Nash equilibrium model with nonlinear budget constraints for which we define the variational equilibrium, which provides us with a variational inequality formulation. We construct an equivalent formulation, enabling the analysis of the influence of the conservation laws and the importance of the associated Lagrange multipliers. We find that the marginal expected transaction utility of each retailer depends on this Lagrange multiplier and its sign. Finally, numerical examples with reported equilibrium product flows, cybersecurity investment levels, and Lagrange multipliers, along with individual firm vulnerability and network vulnerability, illustrate the obtained results.     

Online calibrated forecasts: Memory efficiency versus universality for learning in games

We provide a simple learning process that enables an agent to forecast a sequence of outcomes. Our forecasting scheme, termed tracking forecast, is based on tracking the past observations while emphasizing recent outcomes. As opposed to other forecasting schemes, we sacrifice universality in favor of a significantly reduced memory requirements. We show that if the sequence of outcomes has certain properties—it has some internal (hidden) state that does not change too rapidly—then the tracking forecast is weakly calibrated so that the forecast appears to be correct most of the time. For binary outcomes, this result holds without any internal state assumptions. We consider learning in a repeated strategic game where each player attempts to compute some forecast of the opponent actions and play a best response to it. We show that if one of the players uses a tracking forecast, while the other player uses a standard learning algorithm (such as exponential regret matching or smooth fictitious play), then the player using the tracking forecast obtains the best response to the actual play of the other players. We further show that if both players use tracking forecast, then under certain conditions on the game matrix, convergence to a Nash equilibrium is possible with positive probability for a larger class of games than the class of games for which smooth fictitious play converges to a Nash equilibrium.     

Detecting system failures from durations and binary cues

Durations are often used to judge the status of an invisible process. However, the apparent duration of an interval depends on the actual duration and on other variables, such as the workload during the interval and the person's expectations. An experiment dealt with the use of durations as an information source on the state of an invisible process and the effects of expectations and workload on decisions regarding the process. Eighty-nine participants observed a computerized simulation of a process which could be either intact or faulty, with intact processes ending on average sooner than faulty ones, and they had to indicate whether or not the process is intact and to estimate its duration. A binary cue with either intermediate or no validity indicated whether the process was supposedly intact or not, generating expectations about the duration of the process. Perceived durations and the decisions about the intactness of a process depended on the actual process duration, as well as on the expectations generated by the binary cue. In addition, task workload affected time estimates, but it had no effect on participants' tendency to adhere to cue recommendations or their ability to distinguish between intact and faulty processes. Results show that users' duration-based decisions about the status of a computerized process are affected by internal and external cues. While users can use durations as an information source, they should, whenever possible, be accompanied by additional indicators, lowering the inherent uncertainty in the duration estimation process.     

The longitudinal impact of enterprise system users’ pre-adoption expectations and organizational support on post-adoption proficient usage

Although enterprise systems (ES) are ubiquitous, many firms report less than stellar payoffs from these costly investments, with underutilization often attributed to failures in the implementation process. Unfortunately, research has not provided sufficient insights into these failures, in part because it has focused on actual usage, as opposed to proficient usage, as the benchmark for successful implementation. Moreover, research has not generally examined how the adoption process unfolds over time, thus overlooking potential underlying mechanisms that may help explain how adopters achieve proficiency. To begin addressing these shortcomings, we study how adopters’ pre-adoption expectations, enacted over time, can influence their post-adoption proficiency, by shaping how and why they spend time using the system during the adoption period. We analyzed time-lagged survey data from 153 financial analysts, required to adopt new ES-based software, at a multinational bank. We found that adopters who hold pre-adoption expectations reflecting greater internal and external motives to adopt the system as well as systematically integrate it into their work routines are more apt to use the system in ways that enhance their cumulative knowledge of it, and subsequently develop higher levels of proficiency post-adoption. Moreover, greater organizational support enhanced the impact of adopters’ expectations on proficiency, except when their actual use is low in which case organizational support had an adverse effect.     

Analysis of the dynamics of multi-team Bertrand game with heterogeneous players

In this article, we study the dynamics of a two-team Bertrand game with players having heterogeneous expectations. We study the equilibrium solutions and the conditions of their locally asymptotic stability. Numerical simulations are used to illustrate the complex behaviours of the proposed model of the Bertrand game. We demonstrate that some parameters of the model have great influence on the stability of Nash equilibrium and on the speed of convergence to Nash equilibrium. The chaotic behaviour of the model has been controlled by using feedback control method.     

Open foresight: The influence of organizational context

Open foresight (OF)—a new approach for companies to jointly look into the future—is a response to the limitations of traditional corporate foresight. In an OF process, the companies involved share their understanding and interpretation of future developments. This reduces their uncertainty about the future and helps the companies design and assess development trajectories toward the future, including scenarios, action plans, and innovation ideas. First suggested as a new approach around 2006, OF is still surrounded by many questions. One of these questions concerns the organizational settings needed to enhance the success of OF. This paper focuses on three elements. First, organizational culture has been found to be critical for successful corporate foresight, but no clear evidence on the design of a "foresight‐friendly" culture has so far been presented. Furthermore, top management involvement and commitment has been widely reported as one of the factors of success in innovation processes. What role top management plays in OF has not yet been researched. Finally, OF is a creative process conducted by a team in which all companies involved are represented. In the innovation literature, ample evidence can be found on the importance of team heterogeneity for creativity, but does the same hold for OF processes? Based on an explorative in‐depth case study of an OF process, tentative theory is formulated in the form of four propositions for further research: OF (1) is enhanced by a culture with strong adhocracy and medium weight clan values, (2) requires top management commitment, and (3) is best conducted in a team that is heterogeneous in terms of individual diversity, but (4) homogeneous in terms of management levels involved.