Credibility and Strategic Learning in Networks

This paper studies a model of diffusion in a fixed, finite connected network. There is an interested party that knows the quality of the product or idea being propagated and chooses an implant in the network to influence other agents to buy or adopt. Agents are either “innovators”, who adopt immediately, or rational. Rational consumers buy if buying rather than waiting maximizes expected utility. We consider the conditions on the network under which efficient diffusion of the good product with probability one is a perfect Bayes equilibrium. Centrality measures and the structure of the entire network are both important. We also discuss various inefficient equilibria.

N-Person Bargaining and Strategic Complexity

We investigate the effect of introducing costs of complexity in the n -person unanimity bargaining game. In particular, the paper provides a justification for stationary equilibrium strategies in the class of games where complexity costs matter. As is well-known, in this game every individually rational allocation is sustainable as a Nash equilibrium (also as a subgame perfect equilibrium if players are sufficiently patient and if n > 2). Moreover, delays in agreement are also possible in such equilibria. By limiting ourselves to strategies that can be implemented by a machine (automaton) and by suitably modifying the definition of complexity for the purpose of analysing a single extensive form, we find that complexity costs do not reduce the range of possible allocations but they do limit the amount of delay that can occur in any agreement. In particular, we show that in any n-player game, for any allocation z; an agreement on z at any period t can be sustained as a Nash equilibrium of the machine game with complexity costs if and only if t · n: We use the limit on delay result to establish that, in equilibrium, the machines implement stationary strategies. Finally, we also show that noisy Nash equilibrium” with complexity costs sustain only the unique stationary subgame perfect equilibrium allocation.

Word of Mouth Advertising, Credibility and Learning in Networks

Social networks representing the pattern of social interactions - who talks to or who observes whom- play a crucial role as a medium for the spread of information, ideas, diseases, products. Someone in the population may struck with an infection or may adopt a new technology, and it can then either die out quickly or spread throughout the population, depending possibly on the location of the initial appearance, the structure of the network - for instance, how dense it is. The dynamics of adoption -the extent to which individuals are in uenced by their neighbours, the impact of "word of-mouth" communication- also plays a role in determining the speed of diffusion. Given the large range of contexts in which social learning is important, it is not surprising that researchers from various disciplines have studied processes of diffusion from a variety of perspectives.

Markets with Bilateral Bargaining and Incomplete Information

We study the relationship between bargaining and competition with incomplete information. We consider a model with two uninformed and identical buyers and two sellers. One of the sellers has a privately-known reservation price, which can either be Low or High. The other seller’s reservation price is commonly known to be in between the Low and High values of the privately-informed seller. Buyers move in sequence, and make offers with the second buyer observing the offer made by the first buyer. The sellers respond simultaneously. We show that there are two types of (perfect Bayes) equilibrium. In one equilibrium, the buyer who moves second does better. In the second equilibrium, buyers’ expected payoffs are equalised, and the price received by the seller with the known reservation value is determined entirely by the equuilibrium of the two-player game between a single buyer and an informed seller. We also discuss extensions of the model to multiple buyers and sellers, and to the case where both sellers are privately informed.

When Does Competition Lead to Efficient Investments?

The paper studies agents’ investment decisions between general and speci…c in-vestments under di¤erent ownership structures in a thin, decentralized market where each agent’s decision a¤ects the decisions and welfare of other (otherwise unrelated) agents mainly through indirect market linkages. The paper demonstrates that “excess competition among investors,” in every equilibrium, will lead to e¢cient investments, regardless of asset ownership. In the absence of such excess competition, in every equilibrium, ine¢cient investments will result, unless some special ownership arrange-ment is made. The problem in which the choice variable is investment level, instead of investment type, is also studied.

A simultaneous explanation of the large phase in B_s-\bar B_s mixing and B --> \pi\pi / \pi K puzzles in R-parity violating supersymmetry

Recent data on $B$ meson mixings and decays are, in general, in accord with the standard model expectations, except showing a few hiccups: (i) a large phase in $B_s$ mixing, (ii) a significant difference ($> 3.5 \sigma$) between CP-asymmetries in $B^\pm \to \pi^0 K^\pm$ and $B_d \to \pi^\mp K^\pm$ channels, and (iii) a larger than expected branching ratio in $B_d \to \pi^0\pi^0$ channel. We show that selective baryon number violating Yukawa couplings in R-parity violating supersymmetry can reconcile all the measurements.Comment: 8 pages, 4 eps figs; v2: minor errors corrected, fig.2a redrawn with correct y-axis labels, footnote on updated UTfit result on Bs mixing phase added, References and Acknowledgements sections update

Decentralised bilateral trading in a market with incomplete information

types: ArticleDiscussion paperWe study a model of decentralised bilateral interactions in a small market where one of the sellers has private information about her value. There are two identical buyers and another seller, whose valuation is commonly known to be in between the two possible valuations of the informed seller. We consider two in nite horizon games, with public and private simultaneous one-sided o¤ers respectively and simultaneous responses. We show that there is a stationary perfect Bayes equilibrium for both models such that prices in all transactions converge to the same value as the discount factor goes to 1

Credibility and strategic learning in networks

We analyze a model of diffusion in a fixed, finite connected network. There is an interested party that knows the quality of the product being propagated and chooses an implant in the network to influence other agents to buy. Agents are either “innovators,” who adopt immediately, or rational. Rational consumers buy if buying instead of waiting maximizes expected utility. We consider the conditions on the network under which optimal diffusion of the good product with probability 1 is a perfect Bayes equilibrium