Two-period Colonel Blotto contest with cumulative investments over variable assets with resource constraints

Two resource constrained players compete by investing in two assets which may increase or decrease in value over two periods. A player’s investment in period 1 carries over to period 2. If an asset is cheap in period 1, a player invests more in it in period 1, less in period 2, and does the opposite for the other asset. If an asset is cheap in period 2, a player invests more in it in period 2, less in period 1, and does the opposite for the other asset. If an asset increases in value, both players invest more in it in both periods, and less into the less valuable asset. An advantaged player may invest more into the less valuable asset than the least advantaged player. If an asset increases in value, both players invest more in it in period 2, until the advantaged player eventually ceases investment into the asset with low growth, to focus on the high-growth asset. Various intuitive and less intuitive effects are illustrated for how players strike balances across space (two assets) and time (two periods).