Bidding games with several risky assets and random walks of stock market prices
We consider multistage bidding models where several types of risky assets (shares) are traded between two agents that have different information on the liquidation prices of traded assets. These random prices depend on “a state of nature”, that is determined by the initial chance move according to a probability distribution that is known to both players. Player 1 (insider) is informed on the state of nature, but Player 2 is not. The bids may take any integer values. The
Repeated bidding games were introduced by De Meyer and Saley (2002) to analyze the evolution of the price system at finance markets with asymmetric information. In the paper of De Meyer and Saley arbitrary bids are allowed. It is more realistic to assume that players may assign only discrete bids proportional to a minimal currency unit. This paper represents a survey of author's results on discrete bidding games with asymmetric information.
We investigate a model of one-stage bidding between two differently informed stockmarket agents where one unit of risky asset (share) is traded. The random liquidation price of a share may take two values: the integer positive m with probability p and 0 with probability 1-p. Player 1 (insider) is informed about the price, Player 2 is not. Both players know probability p. Player 2 knows that Player 1 is an insider. Both players propose simultaneously their bids. The player who posts the larger price buys one share from his opponent for this price. Any integer bids are admissible. The model is reduced to zero-sum game with lack of information on one side. We construct the solution of this game for any p and m : we find optimal strategies of both players and describe recurrent mechanism for calculating game value. The results are illustrated by means of computer simulation.
In the article, we attempt to underpin the hypothesis that under certain conditions a propitious selection may take place on the higher education market. It is a phenomenon when brand universities automatically reproduce their positive reputation without improving the quality of teaching due to influx of talented entrants. We apply econometric modelling and regression analysis based on survey of first-year students from Moscow to demonstrate that graduates with high USE marks really prefer to choose among brand universities; moreover, they appreciate a possibility to obtain a prestigious diploma even more than that of acquiring a particular profession. However, entrants do not possess full information about the quality of teaching in a particular university. The analysis presented in the article shows that university rankings do not contribute to overcoming of this information asymmetry, since they transmit distorted signals caused by the methodology of ranking. The rankings, first of all, accentuate academic activity of teachers rather than educational process and interaction with students. For this reason, higher schools often adopt such a strategy to meet the ranking criteria as much as possible; they also tend to improve namely these indicators disregarding the other to become a leader. As a result, brand universities may surpass ordinary universities not due to rendering educational services of higher quality but due to selection of best entrants and peer-effects. These factors allow them to have excellent graduates, thus maintain positive reputation in employers’ opinion and simultaneously raise the brand value by advancing in a ranking.
We describe optimal contest success functions (CSF) which maximize expected revenues of an administrator who allocates under informational asymmetry a source of rent among competing bidders. It is shown that in the case of independent private values rent administrator’s optimal mechanism can always be implemented via some CSFs as posited by Tullock. Optimal endogenous CSFs have properties which are often assumed a priori as plausible features of rent-seeking contests; the paper therefore validates such assumptions for a broad class of contests. Various extensions or optimal CSFs are analyzed.
The paper considers a game-theoretical model of bidding with asymmetric information. One player has the inside information on the liquidation price of risky asset. The model is formalized with the repeated game with incomplete information on the side of uninformed player. We consider the case of external stopping of the game at the random moment. Insider's expected profit in the game of random duration if she applies the strategy optimal in infinite-stage game is obtained. This result allows to calculate the loss of insider in case of sudden disclosure of his private information.
We consider multistage bidding models where two types of risky assets (shares) are traded between two agents that have different information on the liquidation prices of traded assets. These prices are random integer variables that are determined by the initial chance move according to a probability distribution p over the two-dimensional integer lattice that is known to both players. Player 1 is informed on the prices of both types of shares, but Player 2 is not. The bids may take any integer value.
The model of n-stage bidding is reduced to a zero-sum repeated game with lack of information on one side. We show that, if liquidation prices of shares have finite variances, then the sequence of values of n-step games is bounded. This makes it reasonable to consider the bidding of unlimited duration that is reduced to the infinite game G1(p). We offer the solutions for these games.
We begin with constructing solutions for these games with distributions p having two and three-point supports. Next, we build the optimal strategies of Player 1 for bidding games G1(p) with arbitrary distributions p as convex combinations of his optimal strategies for such games with distributions having two- and three-point supports. To do this we construct the symmetric representation of probability distributions with fixed integer expectation vectors as a convex combination of distributions with not more than three-point supports and with the same expectation vectors.