TeamInstantAction is a nickname in the Crysis series given to the infamous "Team DeathMatch" type of game mode. It is, as suggested, a Team oriented version of the InstantAction game mode.
It's rules are simple - Two teams fight against each other, the team with the highest kill count/score at the end of the match is the winner.
Here you'll find the example TeamInstantAction.xml script that is provided with the SDK. Below it you'll find information on what each of these sections mean.
<Mode name='TeamInstantAction'>
<Spawning class='MPRSSpawning' teamGame='1' teamSpawnsType='None' usingLua='0' />
<Scoring class='StandardScoring'>
<Player>
<Event type='PlayerKill' points='200' />
<Event type='PlayerTeamKill' points='0' />
<Event type='PlayerKillAssist' points='40' />
<Event type='Tagged_PlayerKillAssist' points='25' />
</Player>
<Team>
<Event type='PlayerKill' points='1' />
</Team>
</Scoring>
<ScoreRewards enabled='1' />
<AssistScoring class='AssistScoring' maxTimeBetweenAttackAndKillForAssist='7000' maxAssistScore='99' assistScoreMultiplier='0.5' />
<PlayerStats class='StandardPlayerStats' />
<StatsRecording class='StandardStatsRecording' />
<Teams class='StandardTwoTeams' />
<State class='StandardState'>
<StartStrings startMatch='ui_msg_tia_matchstart' />
</State>
<VictoryConditions class='StandardVictoryConditionsTeam' />
<PlayerSetup class='StandardSetup' />
<DamageHandling class='MPDamageHandling'>
<Table path='Scripts/GameRules/MPDamageTable.xml' />
</DamageHandling>
<ActorAction class='MPActorAction' />
<Spectator class='MPSpectator' eatsActorActions='1' enableFree='0' enableFollow='1' enableKiller='1' timeFromDeathTillAutoSpectate='5000' />
</Mode>
Script.ReloadScript("scripts/gamerules/GameRulesUtils.lua");
TeamInstantAction = {};
GameRulesSetStandardFuncs(TeamInstantAction);