Pauli Murto

An Oligopolistic Investment Model of the Finnish Electricity Market

The investment problem faced by producers in deregulated electricity markets contains high uncertainties about the future. It can also be seen as a game, as only a small number of large players act in the market. A dynamic stochastic oligopoly model to describe the production and investment in such a situation is developed and applied to the Finnish electricity market. The demand growth rate is modeled as a stochastic variable. The strategies of the firms consist of investments and production levels for base and peak load periods. The firms have nuclear, hydro and thermal capacities, but are only allowed to invest in new thermal capacity. Using a so-called sample-path adapted open-loop information structure, the model contributes to the understanding of the dynamics of production, investment and market power in a medium time horizon. The solution method uses recent developments in variational inequality and mixed complementarity problem formulations.

A GAME MODEL OF IRREVERSIBLE INVESTMENT UNDER UNCERTAINTY

Most of the literature on real options considers the optimal decision of a firm in isolation from competitors. In reality, however, the actions of competing firms often affect each others investment opportunities. We develop a game model where many firms compete for a single investment opportunity. When one of the firms triggers the investment the opportunity is completely lost for the other firms. The value of the project for the firms is assumed to follow a geometric Brownian motion. The model combines game theory and the theory of irreversible investment under uncertainty. We characterize the resulting Nash equilibrium under different assumptions on the information that the firms have about each others valuations for the project. As an example, we present a case of building a telecommunications network.

Delay and information aggregation in stopping games with private information

We consider equilibrium timing decisions in a model with a large number of players and informational externalities. The players have private information about a common payoff parameter that determines the optimal time to invest. They learn from each other in real time by observing past investment decisions. We develop new methods of analysis for such large games, and we give a full characterization of symmetric equilibria. We show that the equilibrium statistical inferences are based on an exponential learning model. Although the beliefs converge to truth, learning takes place too late. Ex-ante welfare is strictly between that without observational learning and that with full information.

Large common value auctions with risk averse bidders

We analyze large symmetric auctions with conditionally i.i.d. common values and risk averse bidders. Our main result characterizes the asymptotic equilibrium price distribution for the first- and second-price auctions. As an implication, we show that with constant absolute risk aversion (CARA), the second-price auction raises significantly more revenue than the first-price auction. While this ranking seems robust in numerical analysis also outside the CARA specification, we show by counterexamples that the result does not generalize to all risk averse utility functions.

EXIT OPTIONS AND DIVIDEND POLICY UNDER LIQUIDITY CONSTRAINTS

We introduce a post‐entry liquidity constraint to the standard model of a firm with serially correlated profitability and an irreversible exit decision. We assume that firms with no cash holdings and negative cash flow must either exit or raise new cash at a transaction cost. This creates a precautionary motive for holding cash, which must be traded off against the liquidity cost of holding cash. We characterize the optimal exit and payout policy. The direct effect of financial frictions is to impose inefficient exit, but there is also an indirect effect through higher equilibrium price that leads to inefficient survival.

Exit Options and Dividend Policy under Liquidity Constraints

We introduce a post‐entry liquidity constraint to the standard model of a firm with serially correlated profitability and an irreversible exit decision. We assume that firms with no cash holdings and negative cash flow must either exit or raise new cash at a transaction cost. This creates a precautionary motive for holding cash, which must be traded off against the liquidity cost of holding cash. We characterize the optimal exit and payout policy. The direct effect of financial frictions is to impose inefficient exit, but there is also an indirect effect through higher equilibrium price that leads to inefficient survival.

All-pay Auctions with Affiliated Binary Signals

We analyze all-pay auctions with affiliated values and binary signals. We analyze the unique symmetric equilibrium with any number of bidders and show that the bidders earn positive rents only if the equilibrium is monotone. We also characterize the symmetric equilibrium of the closely related two-player war of attrition.

All-Pay Auctions with Affiliated Values

This paper analyzes all-pay auctions where the bidders have affiliated values for the object for sale and where the signals take binary values. Since signals are correlated, high signals indicate a high degree of competition in the auction and since even losing bidders must pay their bid, non-monotonic equilibria arise. We show that the game has a unique symmetric equilibrium, and that whenever the equilibrium is non-monotonic the contestants earn no rents. All-pay auctions result in low expected rents to the bidders, but also induce inefficient allocations in models with affiliated private values. With two bidders, the effect on rent extraction dominates, and all-pay auction outperforms standard auctions in terms of expected revenue. With many bidders, this revenue ranking is reversed for some parameter values and the inefficient allocations persist even in large auctions.

Large all-pay auctions with IPV bidders

This note analyzes different types of all-pay auctions when the number of bidders becomes large. We compute the distributions of the highest bids for the first-price all pay auction and we show that the expected payment made by the winning bidder converges to half of the total payments. In the second-price all-pay auction (the war of attrition), the highest bid amounts to about 35.5% of the total revenues. We also compute the payments for all-pay auctions with multiple prizes.