Mechanisms to Induce Random Choice
Media access protocols in wireless networks require each contending node to wait for a backoff time chosen randomly from a fixed range, before attempting to transmit on a shared channel. However, nodes acting in their own selfish interest may not follow the protocol. In this paper, we use a mechanism design approach to study how nodes might be induced to adhere to the protocol. In particular, a static version of the problem is modeled as a strategic game (the protocol) played by non-cooperating, rational players (the nodes). We present a game which exhibits a unique mixed-strategy Nash equilibrium that corresponds to nodes choosing backoff times randomly from a given range of values, according to any apriori given distribution. We extend this result to the situation when each player can choose a backoff value from a different range, provided there are at least two players choosing from the largest range. In contrast, we show that if there are exactly two players with different backoff ranges, then it becomes impossible to design a strategic game with a unique such Nash equilibrium. Finally, we show an impossibility result under certain natural limitations on the network authority.
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