  This is the first part of a two-part paper that studies the problem of
jamming in a fixed-rate transmission system with fading. Both transmitter and
jammer are subject to power constraints which can be enforced over each
codeword short-term / peak) or over all codewords (long-term / average), hence
generating different scenarios. All our jamming problems are formulated as
zero-sum games, having the probability of outage as pay-off function and power
control functions as strategies. The paper aims at providing a comprehensive
coverage of these problems, under fast and slow fading, peak and average power
constraints, pure and mixed strategies, with and without channel state
information (CSI) feedback. In this first part we study the fast fading
scenario. We first assume full CSI to be available to all parties. For peak
power constraints, a Nash equilibrium of pure strategies is found. For average
power constraints, both pure and mixed strategies are investigated. With pure
strategies, we derive the optimal power control functions for both intra-frame
and inter-frame power allocation. Maximin and minimax solutions are found and
shown to be different, which implies the non-existence of a saddle point. In
addition we provide alternative perspectives in obtaining the optimal
intra-frame power control functions under the long-term power constraints. With
mixed strategies, the Nash equilibrium is found by solving the generalized form
of an older problem dating back to Bell and Cover \cite{bell}. Finally, we
derive a Nash equilibrium of the game in which no CSI is fed back from the
receiver. We show that full channel state information brings only a very slight
improvement in the system's performance.
