Effort, Idiosyncratic Risk and Investment Under Uncertainty

<p>This thesis is based upon four very simple premises: 1. managers, not shareholders make the investment decisions for the firm; 2. managers do more than just say "yes" or "no" to investments, they can also exert effort that affects the payoff from investment; 3. executive compensation schemes can cause managers to hold more stock than is optimal for diversification purposes; and 4. many investments can be delayed and involve irreversible capital costs as well as uncertain payoffs. Combining these four premises gives the two central questions this thesis attempts to answer: 1. How does the level of managerial stock-ownership affect the investment decisions managers make for the firm? and 2. given the answer to (1), how does this affect the shareholder's decision to hire a manager? In this thesis I use a continuous time "Real Options" framework to answer these questions. The form of the utility function assumed for the manager has a huge impact on the tractability of the modelling. The assumption of Constant Relative Risk Aversion (CRRA) utility as opposed to Constant Absolute Risk Aversion (CARA) causes the manager's valuation of the cash flow (the very first step of the modelling) to become wealth dependent. This in itself is an interesting issue, but it also poses interesting numerical issues and makes the later steps of the analysis intractable. Because of this we split the substantive analysis of this thesis into two parts. In the first we assume CARA utility in order to remove wealth dependence from the valuation and obtain a "clean path" to the end goal of a dynamic model of hiring, effort and irreversible investment. In the second we focus on CRRA utility thus allowing the manager's valuation to depend on his financial wealth. We then explain the resultant numerical issues, and the appropriate approach to their solution.</p>

Effort, Idiosyncratic Risk and Investment Under Uncertainty

<p>This thesis is based upon four very simple premises: 1. managers, not shareholders make the investment decisions for the firm; 2. managers do more than just say "yes" or "no" to investments, they can also exert effort that affects the payoff from investment; 3. executive compensation schemes can cause managers to hold more stock than is optimal for diversification purposes; and 4. many investments can be delayed and involve irreversible capital costs as well as uncertain payoffs. Combining these four premises gives the two central questions this thesis attempts to answer: 1. How does the level of managerial stock-ownership affect the investment decisions managers make for the firm? and 2. given the answer to (1), how does this affect the shareholder's decision to hire a manager? In this thesis I use a continuous time "Real Options" framework to answer these questions. The form of the utility function assumed for the manager has a huge impact on the tractability of the modelling. The assumption of Constant Relative Risk Aversion (CRRA) utility as opposed to Constant Absolute Risk Aversion (CARA) causes the manager's valuation of the cash flow (the very first step of the modelling) to become wealth dependent. This in itself is an interesting issue, but it also poses interesting numerical issues and makes the later steps of the analysis intractable. Because of this we split the substantive analysis of this thesis into two parts. In the first we assume CARA utility in order to remove wealth dependence from the valuation and obtain a "clean path" to the end goal of a dynamic model of hiring, effort and irreversible investment. In the second we focus on CRRA utility thus allowing the manager's valuation to depend on his financial wealth. We then explain the resultant numerical issues, and the appropriate approach to their solution.</p>

Integrated Online Learning and Adaptive Control in Queueing Systems with Uncertain Payoffs

Many online service platforms have dedicated algorithms to match their available resources to incoming clients to maximize client satisfaction. One of the key challenges is to balance the generation of higher payoffs from existing clients and exploration of new clients’ unknown characteristics while at the same time satisfy the resource capacity constraints. In “Integrated Online Learning and Adaptive Control in Queueing Systems with Uncertain Payoffs,” Hsu, Xu, Lin, and Bell show that traditional approaches such as maximizing instantaneous payoffs with current knowledge or using queue-length based controls guided by “shadow prices,” would lead to suboptimal long-term payoffs. Instead, they propose a novel utility-guided assignment algorithm that seamlessly integrates online learning and adaptive control to provide high system payoffs with performance guarantees. The theoretical performance bound also lends system design insights into the impact of uncertain client dynamics, payoff learning, and backlogged clients. They further develop a decentralized version of the algorithm, which is applicable to large systems and performs well even when the service rates are random.

The Valuator’s Curse: Decision Analysis of Overvaluation and Disappointment in Acquisition

Initial valuations of entrepreneurial ventures offering uncertain payoffs can often be overvalued by investors; namely, the expected payoff postacquisition is smaller than the expected payoff prior to acquisition when the investor harbors uncertainties about various components of the business. Common explanations involve irrationality such as psychological preference for potential over realized payoffs. We provide a different, rational explanation, which we term the valuator’s curse. It is similar in nature to the winner’s curse in auctions and the optimizer’s curse in decision analysis, but the source of the curse is neither from the competitive effects of an auction-type mechanism nor from the optimization effects in a choice among alternatives. Rather the effect is generated from the nonlinear evaluation of the payoffs, even though the inputs to the evaluation are unbiased. We formalize the valuator’s curse and discuss its implications to entrepreneur’s learning. The valuator’s curse proves a boon to the entrepreneur as it leads to larger capitalizations.

Z-equilibria in Bi-matrix games with uncertain payoffs

The concept of Z-equilibrium has been introduced by Zhuk-ovskii (Mathematical Methods in Operations Research. Bulgarian Academy of Sciences, Sofia (1985) 103–195) for games in normal form. This concept is always Pareto optimal and individually rational for the players. Moreover, Pareto optimal Nash equilibria are Z-equilibria. We consider a bi-matrix game whose payoffs are uncertain variables. By appropriate ranking criteria of Liu uncertainty theory, we introduce some concepts of equilibrium based on Z-equilibrium for such games. We provide sufficient conditions for the existence of the introduced concepts. Moreover, using mathematical programming, we present a procedure for their computation. A numerical example is provided for illustration.

Information Design: A Unified Perspective

Given a game with uncertain payoffs, information design analyzes the extent to which the provision of information alone can influence the behavior of the players. Information design has a literal interpretation, under which there is a real information designer who can commit to the choice of the best information structure (from her perspective) for a set of participants in a game. We emphasize a metaphorical interpretation, under which the information design problem is used by the analyst to characterize play in the game under many different information structures. We provide an introduction to the basic issues and insights of a rapidly growing literature in information design. We show how the literal and metaphorical interpretations of information design unify a large body of existing work, including that on communication in games (Myerson 1991), Bayesian persuasion (Kamenica and Gentzkow 2011), and some of our own recent work on robust predictions in games of incomplete information. ( JEL C70, D82, D83)