Co-design is a prominent topic presently in computing, speaking to the mutual benefit of coordinating design choices of several layers in the technology stack. For example, this may be designing algorithms which can most efficiently take advantage of the acceleration properties of a given architecture, while simultaneously designing the hardware to support the structural needs of a class of computation. The implications of these design decisions are influential enough to be deemed a lottery, enabling an idea to win out over others irrespective of the individual merits. Coordination is a well studied topic in the mathematics of game theory, where in many cases without a coordination mechanism the outcome is sub-optimal. Here we consider what insights game theoretic analysis can offer for computer architecture co-design. In particular, we consider the interplay between algorithm and architecture advances in the field of neuromorphic computing. Analyzing developments of spiking neural network algorithms and neuromorphic hardware as a co-design game we use the Stag Hunt model to illustrate challenges for spiking algorithms or architectures to advance the field independently and advocate for a strategic pursuit to advance neuromorphic computing.