Arieh Gavious

Contracting, signaling, and moral hazard: a model of entrepreneurs, ‘angels,’ and venture capitalists

Abstract Investment by wealthy individuals, known as ‘angels,’ in startup firms is quite significant and has taken off in the last few years. Angels invest in the company at an earlier stage than venture capitalists (VCs) do. This paper examines the relationship between an entrepreneur, an angel, and a VC from the seed investment made by the angel to the exit stage. The study characterizes the equilibrium contracts among the players and provides insights into the related institutional arrangements. Next, the study examines the signaling aspects of the game. The paper also analyzes the moral hazard problems of the entrepreneur and the VC. It shows that the outcome in a startup firm is not efficient because of the free-rider phenomenon.

Explicit Solutions of Optimization Models and Differential Games with Nonsmooth (Asymmetric) Reference-Price Effects

Models in marketing with asymmetric reference effects lead to nonsmooth optimization problems and differential games which cannot be solved using standard methods. In this study, we introduce a new method for calculating explicitly optimal strategies, open-loop equilibria, and closed-loop equilibria of such nonsmooth problems. Application of this method to the case of asymmetric reference-price effects with loss-aversive consumers leads to the following conclusions: (1) When the planning horizon is infinite, after an introductory stage the optimal price stabilizes at a steady-state price, which is slightly below the optimal price in the absence of reference-price effects. (2) The optimal strategy is the same as in the symmetric case, but with the loss parameter determined by the initial reference-price. (3) Competition does not change the qualitative behavior of the optimal strategy. (4) Adopting an appropriate constant-price strategy results in a minute decline in profits.

All-pay auctions with risk-averse players

We study independent private-value all-pay auctions with risk-averse players. We show that: (1) Players with low values bid lower and players with high values bid higher than they would bid in the risk neutral case. (2) Players with low values bid lower and players with high values bid higher than they would bid in a first-price auction. (3) Players’ expected utilities in an all-pay auction are lower than in a first-price auction. We also use perturbation analysis to calculate explicit approximations of the equilibrium strategies of risk-averse players and the seller’s expected revenue. In particular, we show that in all-pay auctions the seller’s expected payoff in the risk-averse case may be either higher or lower than in the risk neutral case.

Location of terror response facilities : A game between state and terrorist

Abstract We study a leader follower game with two players: a terrorist and a state where the later one installs facilities that provide support in case of a terrorist attack. While the Terrorist attacks one of the metropolitan areas to maximize his utility, the State, which acts as a leader, installs the facilities such that the metropolitan area attacked is the one that minimizes her disutility (i.e., minimizes ‘loss’). We solve the problem efficiently for one facility and we formulate it as a mathematical programming problem for a general number of facilities. We demonstrate the problem via a case study of the 20 largest metropolitan areas in the United States.

Revenue equivalence in asymmetric auctions

Abstract The Revenue Equivalence Theorem is generalized to the case of asymmetric auctions in which each players valuation is drawn independently from a common support according to his/her distribution function.

A restricted complete sharing policy for a stochastic knapsack problem in B-ISDN

Consider a circuit switched broadband ISDN network that support a variety of traffic classes (e.g., data, voice, video, facsimile), each of which has its own traffic requirement and reward function. We address the problem of dynamically allocating the capacity of each circuit among the traffic classes. As an optimal allocation policy is extremely hard to find, we apply a different methodology by which we bound from above the optimal expected reward, and propose a specific threshold policy-the restricted complete sharing (RCS)-that yields a reward sufficiently close to this bound. The initial parameters of the threshold policy are found with the aid of our bounding technique, and are improved by two iterative procedures. The quality of our policy is demonstrated by several numerical examples. >

The dynamics of price elasticity of demand in the presence of reference price effects

The authors derive an expression for the price elasticity of demand in the presence of reference price effects that includes a component resulting from the presence of gains and losses in consumer evaluations. The effect of reference price is most noticeable immediately after a price change, before consumers have had time to adjust their reference price. As a result, immediate-term price elasticity is higher than long-term elasticity, which describes the response of demand long after a price change, when reference price effects are negligible. Furthermore, because of the differential effect of gains and losses, immediate-term price elasticity for price increases and price decreases is not equal. The authors provide a quantitative definition for the terms immediate term and long term, using the average interpurchase time and the discrete “memory” parameter. Practical consequences of the distinction between immediate- and long-term elasticities for the estimation and use of elasticity values are discussed.

A multi-period game theoretic model of venture capitalists and entrepreneurs

As venture capitalists (VCs) have an important role in financial start-ups, most studies have focused on venture capital as a short-term source of financing. The authors examine the relation between a VC and an entrepreneur in a multi-period game in which the contract is set at the beginning of the game, and follows the relation from its start to the end. This multi-period game theoretic model focuses on the problem of moral hazard – the entrepreneurs hidden effort and how a VC can cope with it, using staged investments. First a game between a VC and an entrepreneur is presented, in which the VC is unable to notice the entrepreneur’s effort. Next, a multi-period game between the parties is examined, where the contract is established at the beginning of the multi-period game. The results of the model are presented, and several propositions and theorems are advanced. The multi-period aspects of the model allow for deriving the strategic behavior of the VCs and entrepreneurs over time. The model is consistent with reality, where the average duration of the relation between venture capitalists and entrepreneurs is several years and the investment is made in stages. The study provides insights on optimal contracts and the characterization of an endogenous exit point. It is suggested that the optimal incentive scheme back load all incentive payments to the entrepreneur, and a straight debt contract is optimal in venture financing. Recommendations are made for further studies on the contracts among VCs who syndicate together, as well as the bargaining between the VC and the entrepreneur.(CBS)

Low and high types in asymmetric first-price auctions

Abstract We study first-price auctions with n bidders where bidders’ types (valuations for the object) are drawn independently according to heterogeneous distribution functions. We show a relation between the distributions of high types and their equilibrium bids. On the other hand, we show that there is no relation between the distributions of types and equilibrium bids of low types, i.e. the equilibrium bids of low types are invariable.

Incentives' Effect in Influenza Vaccination Policy

In the majority of developed countries, the level of influenza vaccination coverage in all age groups is suboptimal. Hence, the authorities offer different kinds of incentives for people to become vaccinated such as subsidizing immunization or placing immunization centers in malls to make the process more accessible. We built a theoretical epidemiological game model to find the optimal incentive for vaccination and the corresponding expected level of vaccination coverage. The model was supported by survey data from questionnaires about peoples perceptions about influenza and the vaccination against it. Results suggest that the optimal magnitude of the incentives should be greater when less contagious seasonal strains of influenza are involved and greater for the nonelderly population rather than the elderly, and should rise as high as