The analysis of player's behaviour in modified ‘sea battle’ game

The well-known ‘Sea battle’ game is in the focus of the current job. The main goal of the article is to provide modified version of ‘Sea battle’ game and to find optimal players strategies in the new rules. Changes were applied to attacking strategies (new option to attack hitting four cells in one shot was added) as well as to the size of the field (sizes of $10 \times 10$, $20 \times 20$, $30 \times 30$ were used) and tot he rules of disposal algorithms during the game (new possibility to move the ship off the attacking zone). The game was solved with the use of game theory capabilities: payoff matrices were found for each version of altered rules, for which optimal pure and mixed strategies were discovered. For solving payoff matrices iterative method was used. The simulation was in applying five attacking algorithms and six disposal ones with parameters variation due to the game of players with each other. Attacking algorithms were varied in $100$ sets of parameters, disposal algorithms — in $150$ sets. Major result is that using such algorithms the modified ‘Sea battle’ game can be solved — that implies the possibility of finding stable pure and mixed strategies of behaviour, which guarantee the sides gaining optimal results in game theory terms. Moreover, influence of modifying the rules of ‘Sea battle’ game is estimated. Comparison with prior author's results on this topic was made. Based on matching the payoff matrices with the statistical analysis, completed earlier, it was found out that standard ‘Sea battle’ game could be represented as a special case of game modifications, observed in this article.The job is important not only because of its applications in war area, but in civil areas as well. Use of article's results could save resources in exploration, provide an advantage in war conflicts, defend devices under devastating impact.