Minimax regret treatment choice with covariates or with limited validity of experiments

This paper continues the investigation of minimax regret treatment choice initiated by Manski (2004). Consider a decision maker who must assign treatment to future subjects after observing outcomes experienced in a sample. A certain scoring rule is known to achieve minimax regret in simple versions of this decision problem. I investigate its sensitivity to perturbations of the decision environment in realistic directions. They are as follows. (i) Treatment outcomes may be influenced by a covariate whose effect on outcome distributions is bounded (in one of numerous probability metrics). This is interesting because introduction of a covariate with unrestricted effects leads to a pathological result. (ii) The experiment may have limited validity because of selective noncompliance or because the sampling universe is a potentially selective subset of the treatment population. Thus, even large samples may generate misleading signals. These problems are formalized via a “bounds” approach that turns the problem into one of partial identification.In both scenarios, small but positive perturbations leave the minimax regret decision rule unchanged. Thus, minimax regret analysis is not knife-edge-dependent on ignoring certain aspects of realistic decision problems. Indeed, it recommends to entirely disregard covariates whose effect is believed to be positive but small, as well as small enough amounts of missing data or selective attrition. All findings are finite sample results derived by game theoretic analysis.     

Stopping with congestion and private payoffs

This paper analyses a two-player stopping game with multiarmed bandits in which each player chooses between learning about the quality of her private risky arm and competing for the use of a single shared safe arm. The qualities of the players’ risky arms are independent. A player whose risky arm produces a success no longer competes for the safe arm. We assume that a player observes her opponent’s actions but not his realised payoffs. She is therefore never certain whether her opponent is still competing for the safe arm. When the players’ prior probabilities of success are sufficiently close, there exists no pure strategy equilibrium, and we characterise the unique mixed strategy equilibrium. Otherwise, the unique equilibrium is in pure strategies. The amount of experimentation performed in equilibrium is inefficiently low but, for many priors, higher than if successes are publicly observed.     

Solving the incomplete markets model with aggregate uncertainty by backward induction

This paper describes a method to solve models with a continuum of agents, incomplete markets and aggregate uncertainty. I use backward induction on a finite grid of points in the aggregate state space. The aggregate state includes a small number of statistics (moments) of the cross-sectional distribution of capital. For any given set of moments, agents use a specific cross-sectional distribution, called “proxy distribution”, to compute the equilibrium. Information from the steady state distribution as well as from simulations can be used to chose a suitable proxy distribution.     

Experiential regret in service failure: The role of service justices

ABSTRACT

Regret is so common as to be the second most frequently named emotion in a study of the use of emotions in everyday language (Shimanoff, 1984 Shimanoff, S. B. (1984). Commonly named emotions in everyday conversations. Perceptual and Motor Skills, 58, 514. doi:10.2466/pms.1984.58.2.514[Crossref], [Web of Science ®] , [Google Scholar]). Regret is a negative, cognitively based emotion that we experience when realizing or imagining that our present situation would have been better had we acted differently (Zeelenberg, 1999 Zeelenberg, M. (1999). The use of crying over spilled milk: A note on the rationality and functionality of regret. Philosophical Psychology, 12, 325–340. doi:10.1080/095150899105800[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). Meanwhile, complaint handling takes an important role in raising the retention rate of the customers who experience service problems (Hart, Heskett, & Sasser, 1990 Hart, C. W. L., Heskett, J. L., & Sasser, W. E., Jr. (1990). The profitable art of service recovery. Harvard Business Review, 68(4), 148–156.[PubMed], [Web of Science ®] , [Google Scholar]). Customers anticipate that enterprises will remedy their service failure. The complaining process enhances the relationship between dissatisfied customers and enterprises (Chebat & Slusarczyk, 2005 Chebat, J. C., & Slusarczyk, W. (2005). How emotions mediate the effects of perceived justice on loyalty in service recovery situations: An empirical study. Journal of Business Research, 58, 664–673. doi:10.1016/j.jbusres.2003.09.005[Crossref], [Web of Science ®] , [Google Scholar]). One of the strategies to retain customers is to recover justice from failures (Blodgett, Hill, & Tax, 1997 Blodgett, J. G., Hill, D. J., & Tax, S. S. (1997). The effects of distributive, procedural, and interactional justice on postcomplaint behavior. Journal of Retailing, 73(2), 185–210. doi:10.1016/s0022-4359(97)90003-8[Crossref], [Web of Science ®] , [Google Scholar]). This study intended to explore the impact of customers’ experiential regret in service failure on customers’ behavioral intention and investigate whether the service justice perceived by customers moderates the relationship between these two.     

Uncertain information structures and backward induction

In everyday economic interactions, it is not clear whether each agent’s sequential choices are visible to other participants or not: agents might be deluded about others’ ability to acquire, interpret or keep track of data. Following this idea, this paper introduces uncertainty about players’ ability to observe each others’ past choices in extensive-form games. In this context, we show that monitoring opponents’ choices does not affect the outcome of the interaction when every player expects their opponents indeed to be monitoring. Specifically, we prove that if players are rational and there is common strong belief in opponents being rational, having perfect information and believing in their own perfect information, then, the backward induction outcome is obtained regardless of which of her opponents’ choices each player observes. The paper examines the constraints on the rationalization process under which reasoning according to Battigalli’s (1996) best rationalization principle yields the same outcome irrespective of whether players observe their opponents’ choices or not. To this respect we find that the obtention of the backward induction outcome crucially depends on tight higher-order restrictions on beliefs about opponents’ perfect information. The analysis provides a new framework for the study of uncertainty about information structures and generalizes the work by Battigalli and Siniscalchi (2002) in this direction.     

WHAT HAPPENED TO THE THREE‐LEGGED CENTIPEDE GAME?

Abstract.  In the last two decades, several frameworks have been proposed to analyze the question of whether common knowledge of rationality is sufficient to justify the play of backward induction (BI) in games of perfect information. Three strands of literature have addressed this issue: the literature on equilibrium refinements, the literature on knowledge-based epistemology and the literature on interactive epistemology. This paper surveys seminal frameworks within the first two strands of research and assesses the extent to which they provide a satisfactory solution to the problem. These approaches are illustrated using a three-legged version of Rosenthal's centipede game, which is the classical example in the literature. The paper argues that some of these frameworks provide sensible answers to the riddle of BI or, at least, succeed in bringing the paradox to another level. The paper also points at consistency problems in the body of refinements of Nash equilibrium revealed by the surveyed literature.     

Restricting capital outflow

According to the “Capital Asset Pricing Model”, an individual can increase his utility by diversifying his capital across countries. If that is the case, then why do governments impose restrictions on capital outflow? This paper argues that foreign owners of capital have less political power than domestic ones and therefore capital liberalization weakens the political power that protects capital, increases the taxation of capital and thus reduces total investment. Indeed, most of the empirical evidence suggests that capital liberalization is positively correlated with government expenditure, social security spending and corporate taxation.     

Option hedging theory under transaction costs

The problem of option hedging in the presence of proportional transaction costs can be formulated as a singular stochastic control problem. Hodges and Neuberger [1989. Optimal replication of contingent claims under transactions costs. Review of Futures Markets 8, 222–239] introduced an approach that is based on maximization of the expected utility of terminal wealth. We develop a new algorithm to solve the corresponding singular stochastic control problem and introduce a new approach to option hedging which is closer in spirit to the pathwise replication of Black and Scholes [1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–654]. This new approach is based on minimization of a Black–Scholes-type measure of pathwise risk, defined in terms of a market delta, subject to an upper bound on the hedging cost. We provide an efficient backward induction algorithm for the problem of cost-constrained risk minimization, whose associated singular stochastic control problem is shown to be equivalent to an optimal stopping problem. This algorithm is then modified to solve the singular stochastic control problem associated with utility maximization, which cannot be reduced to an optimal stopping problem. We propose to choose an optimal parameter (risk-aversion coefficient or Lagrange multiplier) in either approach by minimizing the mean squared hedging error and demonstrate that with this “best” choice of the parameter, both approaches have similar performance. We also discuss the different notions of risk in both approaches and propose a volatility adjustment for the risk-minimization approach, which is analogous to that introduced by Zakamouline [2006. European option pricing and hedging with both fixed and proportional transaction costs. Journal of Economic Dynamics and Control 30, 1–25] for the utility maximization approach, thereby providing a unified treatment of both approaches.     

Valuation of stock loans with jump risk

A stock loan is a special loan with stocks as collateral, which offers the borrowers the right to redeem the stocks on or before the maturity (Xia and Zhou, 2007, Dai and Xu, 2011). We investigate pricing problems of both infinite- and finite-maturity stock loans under a hyper-exponential jump diffusion model. In the infinite-maturity case, we derive closed-form formulas for stock loan prices and deltas by solving the related optimal stopping problem explicitly. Moreover, we obtain a sufficient and necessary condition under which the optimal stopping time is finite with probability one. In the finite-maturity case, we provide analytical approximations to both stock loan prices and deltas by solving an ordinary integro-differential equation as well as a complicated non-linear system. Numerical experiments demonstrate that the approximation methods for both prices and deltas are accurate, fast, and easy to implement.     

On the closed-form solution of an endogenous growth model with anticipated consumption

This paper derives a closed-form solution of the AK endogenous growth model with logarithmic preferences and anticipated future consumption which enters additively into effective consumption. We get an explicit representation of the time paths of the economic variables in level by resorting to Gaussian Hypergeometric functions. We compare the model with anticipated future consumption to the model with habit formation. The maximum utility attainable in the model with anticipation is shown to be higher than the one attainable in the model with habits. Using the derived explicit expressions, we perform some comparative-dynamics and -statics analyses with respect to relevant parameters. Numerical simulations complement the theoretical results. Thus, this work provides further support to the usefulness of especial functions in the study of economic dynamics.     

Self-coordination in time inconsistent stochastic decision problems: A planner–doer game framework

Time inconsistency has been a thorny issue in many economic and financial decision making problems, especially when risk measures are involved in performance criteria. We develop in this paper a two-tier planner–doer game framework with self-coordination. By aligning the global interest of the planner and the local interests of the doers by applying suitable penalty functions, a degree of internal harmony (measured quantitatively by the expected cost of self-coordination) can be achieved by the self-coordination policy. We establish an axiom system for modified preferences, under which the self-coordination policy can be obtained by solving a corresponding optimization problem. We then apply our game framework successfully in dynamic mean-variance portfolio selection.     

Admissible and minimax estimators of 363-1363-1363-1in the gamma distribution with truncated parameter space

In this paper we consider asmissible and minimax estimation of the parameter in the gamma distribution with truncated parameter space. We give a necessary and sufficient condition for minimaxity (Theorem 1) and obtain the classes of new minimax and asmissible estimators. The results of the paper can be applied to estimation of parameters in the normal, lognormal, Pareto, generalized gamma, generalized Laplace and other distributions.     

Coalitional stability in the location problem with single-dipped preferences: An application of the minimax theorem

This study considers a situation in which agents choose the location of a public facility from a street according to a given mechanism. Agents have single-dipped preferences over a set of feasible locations. We analyze coalitional behavior for any given mechanism for this situation. We identify a necessary and sufficient condition for a mechanism to possess a strong Nash equilibrium by applying the minimax theorem of von Neumann and Morgenstern (1944). We introduce a class of core solutions and show that these solutions are characterized by strong Nash implementability. As a byproduct of these results, we propose a simple mechanism that implements any core solution in strong Nash equilibria.     

Using dynamic programming with adaptive grid scheme for optimal control problems in economics

The study of the solutions of dynamic models with optimizing agents has often been limited by a lack of available analytical techniques to explicitly find the global solution paths. On the other hand, the application of numerical techniques such as dynamic programming to find the solution in interesting regions of the state was restricted by the use of fixed grid size techniques. Following Grüne (Numer. Math. 75 (3) (1997) 319; University of Bayreuth, submitted, 2003), in this paper an adaptive grid scheme is used for finding the global solutions of discrete time Hamilton–Jacobi–Bellman equations. Local error estimates are established and an adapting iteration for the discretization of the state space is developed. The advantage of the use of adaptive grid scheme is demonstrated by computing the solutions of one- and two-dimensional economic models which exhibit steep curvature, complicated dynamics due to multiple equilibria, thresholds (Skiba sets) separating domains of attraction and periodic solutions. We consider deterministic and stochastic model variants. The studied examples are from economic growth, investment theory, environmental and resource economics.     

Dynamic agency with persistent observable shocks

This paper studies a continuous-time hidden-action model with persistent observable shocks. In this model, I develop a method to characterize the optimal contract with history-dependent effort exertion and shirking decisions. Temporal shirking is always optimal after some histories as long as a positive persistent shock is expected. As a result, my model gives rise to a mechanism through which the moral hazard problem amplifies macroeconomic fluctuations. I also show the pattern of the agent’s utility adjustments with respect to persistent shocks and its implications for compensation design.     

Good signals gone bad: Dynamic signalling with switched effort levels

This paper examines signalling when the sender exerts effort and receives benefits over time. Receivers only observe a noisy public signal about the effort, which has no intrinsic value.The modelling of signalling in a dynamic context gives rise to novel equilibrium outcomes. In some equilibria, a sender with a higher cost of effort exerts strictly more effort than his low-cost counterpart. The low-cost type can compensate later for initial low effort, but this is not worthwhile for a high-cost type. The interpretation of a given signal switches endogenously over time, depending on which type the receivers expect to send it.     

《云南映象》——分析民族舞蹈产业化现象

本文以《云南映像》大型原生态民族舞蹈的产业化运营方式为研究对象,通过对《云南映象》的产业化历程进行具体分析,就民族民间舞蹈文化如何在市场经济的调节下走出一条适应于本土民族舞蹈文化发展的产业化道路提出几点见解。     

Dynamic competition with consumer inertia

We study a framework where two duopolists compete repeatedly in prices and where chosen prices potentially affect future market shares, but certainly do not affect current sales. This assumption of consumer inertia causes (noncooperative) coordination on high prices only to be possible as an equilibrium for low values of the discount factor. High discount factors increase opportunism and aggressiveness of competition to such an extent that high prices are no longer sustainable as an equilibrium outcome. Moreover, we find that both monopolization and enduring market share and price fluctuations (price wars) can be equilibrium path phenomena without requiring exogenous shocks in market or firm characteristics.     

Optimization in a Dynamic Leontief Model with Restricted Value Growth

The purpose of this paper is to develop a dynamic Leontief model of an msector economic system in which the production of all goods requires one time period and one primary factor, but no capital stocks of any good, and in which the total value of outputs from all sectors is required to grow at a specified rate in each period. The requirement of a fixed rate of total value growth is less restrictive than the familiar condition of balanced growth across all sectors, and it permits the definition and analysis of interesting finite-period optimization problems. Specific results of the paper include the following: (1) the proof that a value-added maximization problem with an unrestricted initial state will experience consumption in exactly one sector in each time period, and willyield an optimal value function which is linear in the variables that describe the terminal state of the system; (2) the development of an efficient Dantzig-Wolfe procedure for analysis of the total value-added maximization problem where both the initial and terminal states are specified; (3) the derivation of testable properties that will guarantee the attainability of a specified target state from a specified initial state of the system; (4) a formal comparison of some basic characteristics of total value growth and balanced value growth.     

Irreversible investment and capacity choice with Bayesian learning

This paper incorporates information incompleteness into the standard capacity choice model. The firm dynamically updates its belief about the expected growth rate based on the realization of demand shocks. First, the firm’s expansion decision becomes more conservative in the dynamic updating case. Moreover, a myopic firm always overestimates the marginal value of capital but underestimates firm value. When we decompose the firm value into the value of assets in place and growth opportunities, dynamic learning significantly increases the value of growth opportunities rather than that of assets in place. Finally, the implications for the user cost of capital is also examined.