Libor rate manipulation & optimal design: A model of non-cooperative strategic behavior

We present an incomplete-information, non-cooperative game-theoretic model that mimics the LIBOR rate formation process. Each player (bank) receives a private iid signal about the state of the world. Players' strategies are mappings from their signals to interest-rate announcements; the LIBOR interest rate is determined as a trimmed mean of all bank announcements. Each bank is characterized by a commonly known idiosyncratic bias parameter, reflecting its portfolio exposure to LIBOR-pegged assets: banks with positive (negative) biases attempt to distort LIBOR above (below) the value that would result if all players acted non-strategically.
We prove that when players' priors over the state of the world are diffuse, there exists a pure strategy equilibrium in which players' announcements differ from their signals by a scalar manipulation parameter. We show that in general a given set of biases may be consistent with multiple equilibria, some of which exhibit the property that banks' strategies are non-monotone in their biases--i.e., banks with higher bias parameters can have lower manipulation parameters. On the other hand, if all banks' bias parameters are sufficiently small, the Nash equilibrium is unique. For games in this class, we study the comparative statics properties of players' strategies with respect to changes in model primitives. We show that the value of each bank's manipulation parameter unambiguously increases in its own bias and decreases in all other banks' biases. We also examine the effects of changing the structure of the LIBOR rate formation process. We find that increasing the size of the bank panel leads to greater rate manipulation, while adopting a stricter trimming rule reduces rate manipulation. On the other hand, stricter trimming rules increase the variance of the gap between realized LIBOR and the true state of the world.
Our results are surprisingly pessimistic about the possibility of designing survey-based measures like the LIBOR or EURIBOR in ways that are robust to manipulation. Even for the simple class of equilibria that we study, we show that the welfare implications of changing the size of the panel or adopting stricter trimming are in general ambiguous, and that the optimal way to structure the LIBOR rate setting process is highly sensitive to the distribution of bank biases. Our model thus lends support to recent proposals that any survey-based measure should be complemented with audits of actual bank borrowing costs.
Our paper concludes with some remarks about implications of alternate behavioral models such as collusion, and considers the scope for policies such as asymmetric trimming of bank reports.