To run or not?: Some dynamic programming models in cricket

In cricket, particularly near the end of an innings, batsmen of different abilities need to manage the rate at which they score runs. Either batsman can choose to bat aggressively or defensively, which alters their chances of scoring runs or being dismissed. Since they change ends when they score a run and at the end of an over, by scoring an odd or even number of runs the two batsmen also determine which of them will face the next ball. It may be worthwhile to refuse a run to keep the slower or lower scoring batsman from the strike. Some dynamic programming models are developed which could be used to maximise the total number of runs scored.