Playing against an Apparent Opponent: Incentives for Care, Litigation, and Damage Caps under Self-Serving Bias
The collecton contains paper accepted for the Seventh International Conference Game theory and Management (June 26-28, 2013, St. Petersburg State University, St. Petersburg, Russia). The presented papers belong to the field of game theory and its application to mamagement.
The volume may be recommended for researchers and post-graduate students of management, economic and applied mathematics departments.
Sited and reviewed in: Math-Net.Ru and RSCI. Abstracted and indexed in: Mathematical Reviews, Zentralblatt MATH and VINITI.
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.
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.
The paper proposes a list of requirements for a game able to describe individually motivated social interactions: be non-cooperative, able to construct multiple coalitions in an equilibrium and incorporate intra and inter coalition externalities. For this purpose the paper presents a family of non-cooperative games for coalition structure construction with an equilibrium existence theorem for a game in the family. Few examples illustrate the approach. One of the results is that efficiency is not equivalent to cooperation as an allocation in one coalition. Further papers will demonstrate other applications of the approach.
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.
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.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.