Signal jamming model

Signal jamming models appeared in the United States in the mid-1980s. With the help of game theory instruments, they examine the noisy communication game between sender and receiver.

structure

The simplest case of a signal jamming model describes communication between just two players. The sender has an information advantage and would like to use its signal to influence the expectations and actions of the signal recipient. He does this because the latter influence his own utility function. From the point of view of the recipient, the noisy - and possibly distorted - signal from the sender is at least partially credible, as the distortion of the private signal is associated with costs for the sender. In order to get this problem under control analytically, assumptions about the target function of the sender, its risk preference and the distribution of the report size are necessary. As a rule, risk neutrality is assumed. This assumption ensures that no risk premiums have to be taken into account. A typical objective function of the sender would be the following:

${\ displaystyle U = x \ cdot P - {\ frac {cb ^ {2}} {2}}}$

${\ displaystyle U}$ Benefit of the transmitter

${\ displaystyle x}$ Weighting of the price in the sender's utility function

${\ displaystyle P}$ Market price

${\ displaystyle c}$ Marginal cost of distortion

${\ displaystyle b = yr}$ Bias, deviation in the report from the private signal ${\ displaystyle r}$ ${\ displaystyle y}$

It is often assumed that all random variables are normally distributed. The example given here is based on the article by Fisher and Verrecchia 2000. There, the manager of a company transmits a signal to the capital market, which is perceived as a player, of the true company value . ${\ displaystyle {\ tilde {y}} \ sim N (0, \ sigma _ {y} ^ {2})}$ ${\ displaystyle {\ tilde {v}} \ sim N (0, \ sigma _ {v} ^ {2})}$

balance

In equilibria with rational expectations , all players have rational ones and that means mathematically correct expectations here. In particular, the recipient knows the sender's decision-making situation. Conversely, the sender also knows what information the recipient has.

literature

Fischer, PE / Verrecchia, R. (2000), Reporting Bias, in: The Accounting Review, pp. 9-4.
Fischer, PE / Stocken, PC (2004), Effect of Investor Speculation on Earnings Management, in: Journal of Accounting Research, Vol. 4.